iiectriciU
/.•ETAYRTON.F.K.S
JOSEPH GALE
\Late T. T, MAKKHAM),
Telejpap5 Enjineei' aqd EleeMcian,
102, FETTER LANE, E.G.
Manufacturer and Fixer of Electric Bells,
Fire, Thief, and Burglar Alarms,
Lightning Conductors, Apparatus for Lighting Gas
by Electricity,
Pneumatic Bells, Speaking Tubes, etc.
N.B. — AH kinds of Desk and other Rails to order.
«sc iSEinrT,
(.'o^&r 2.]
AD VER TISEMENTS.
Electrical and Scientific
Apparatus and Materials.
Immense Stock.
ELECTRIC BELLS, WIRES,
INDICATORS,
CARBONS, CLAMPS,
PHYSICAL
APPARATUS.
NEW
Inductive
Machines <k N^qf y. .^ .
Experiments. >>^,/t>^^^
COILS & BATTERIES. \^
Electric Light Fittings
and Appliances.
Photographic and Optical Goods.
Send for Illustrated Catalog aes^ N^ X.
a guide to purchasers and the most >s^^ ^^
complete in the trade, N/ ^y
26, LUDGATB HILL, LONDON, E.G.
GASSNER'S DRY BATTERY.
WHOLESALE DEPOT:
MAYFIELD, COBB^ & CO., LIMITED,
4il and 35a^ Queen Victoria Street^ London.
Many so-called dry elements have been introduced from time to time, but the faults
in thtm have been such as to prevent their being brought into general use, notwithstand-
ing the desirability of such a Cell for many purposes ; in the Gassner Dry Ce 1 all ihe
previous difficulties have been overcome, and we now possess a perfect dry Cell. 'I'ne
Gassner Dry Cell has been on its trial for nearly two years, and is already approved and
extensively used by electricians, both in this country and abroad, in place of the
Leclanche Cell, of which it possesses all the advantages without sharing its deficiencies.
Its form is more compact than the Leclanche, it will work as long a time from beginning
to end, and gives a more constant current.
The Cells are supplied ready for use, and will work well until completely exhausted ;
they require no cleaning of the zincs, or renewal of the sal-ammoniac ; this renders the
Battery cheaper and more pleasant to use ; and then, as a still further advantage, after
being completely exhausted the Cells can be completely renovated (indeed it is said the
condition is then even better than at first) by passing the current from Bunsen's Cells, in
a similar manner to the charging of a storage Battery.
The Gassner Cells can be put into any position, upr'ght, upside down, or on their
sides, whichever may be most convenient ; they may be used in places subject to high
temperatures, gas factories, boiler rooms, &c., and they are not affected by severe cold ;
when at rest no chemical action takes place.
WRITE FOR FURTHER PARTICULARS [2
To face Cover 2.] iii
AD VERTISEMENTS.
Robey & Co.'s High Speed Engines & Dynamo —
Horizontal and Vertical.
Economy in Fuel.
Regularity in Hunning.
O
Face Title.
[Prac. Electric.
PRACTICAL ELECTRICITY
LABORATORY AND LECTURE COURSE,
For First Year Students of Electrical Engineering^
BASED ON THE
Practical Definitions of the Electrical Units.
BY
W. E. AYRTON, F.R.S.,
Assoc. Mem. Inst. C.E.,
PECFESSOB OF API'LIKD PHYSICS AT THE CITY AND GUILDS OF LONDON
CENTRAL INSTITUTION.
WITH NVilEROVS ILLUSTRATIONS.
iFiftf) enttion.
CASSELL & COMPANY, Limited
LONDOJH, PARIS d- MELBOURNE.
1891.
[all BIGHTS RESEKVk.D.1
PEEFACE.
This book is intended to assist students in acquiiing
experimentally an exact working knowledge of electric
current, difference of potentials, resistance, electromotive
force, quantity, capacity, and power. It does not merely
contain short instructions for the carrying out of experi-
ments such as may be found in existing books on practical
physics, nor, on the other hand, does it resemble certain
text-books, mainly of value as electrical dictionaries,
which give a little information about everything that
can be comprised under the head of electricity, whether
it be electric eels, the history of the invention of the
telegraph, the aurora, or the earliest forms of frictional
machines.
During the past few years I have been gradually
developing a three years' laboratory and lecture course
for students of electrical technology, and this book com-
prises the substance of the first year's course, together
witli some additional matter, mainly in small print.
Experience has shown me that after a student has gone
intelligently through this course, under proper direction,
he has obtained clear notions of the meaning of the
ainpere, the volt, the ohm, the coulomb, the farad, and
the watt, and feels himself familiar with their connection
with one another, and with the modes of employing them
in actual practice. He has, in fact, mastered the basis
of the exact commercial measurement of electrical quan-
tities. It is to be hoped, therefore, that this book may
be useful to other teachers as a basis of a j)Tactical course
of instruction ; and on that account I have given, at the
end, two or three samples of the actual instructions
IV PRACTICAL ELECTRICITV.
which are attached to the sets of apparatus at the City
and Guilds of London Central Institution.
The subjects of magnetism, electro-magnetism, dy-
namo machines, electromotors, self-induction, &c., are but
very briefly referred to, because the experimental treat-
ment of these subjects, which forms my course for
second-year students, will be found in a subsequent book
on " Practical Magnetism."
One of the great difficulties experienced by people in
mastering the quantitative science of electricity, arises
from the fact that we do not number an electrical sense
omong our other senses, and hence we have no intuitive
perception of electrical phenomena. During childhood
we did not have years of unconscious experimenting
with electrical forces as we had with the forces connected
with the sensations of heaviness and lightness, loudness
and softness, heat and cold. Beyond a shock or two
taken perhaps from some medical galvanic apparatus, or
from a Leyden jar, our senses have never been afifected
by electrical action, and hence we ought to begin the
study of electricity as a child begins its early education.
Quite an infant has distinct ideas about hot and cold,
although it may not be able to put its ideas into words,
and yet many a student of electricity of mature years
has but the haziest notions of the exact meaning of high
and low potential, the electrical analogues of hot and
cold. That it is desirable that students should learn
physics, as they learn to ride the bicycle^ by experiment-
ing themselves, is now generally admitted, and this is
especially true in the case of electricity, since it is by
experimenting, and only by experimenting, that a student
can obtain such a real grasp of electricity that its laws
become, so to say, a part of his nature.
Hence, in the courses of electricity which I arranged
at the City, and Guilds of London Technical College,
Finsbury, and at their Central Institution, for every
hour that a student spends at lecture, he spends several
ui the laboratory.
PREFACE. V
Readers who have been accustomed only to the ordi-
nary books, commencing with certain chapters on statical
electricity, continuing with one or more on magnetism,
and ending with some on current electricity, will be
surprised at the arrrangement of the subjects in this
book, and will probably be astonished at what they will
condemn, at the first reading, as a total want of order.
But so far from the various subjects having been thrown
together hap-hazard, the order in which they have been
arranged has been a matter of the most careful considera-
tion, and has been arrived at by following what appears
to me to be the natural as distinguished from the scho-
lastic method of stiidying electricity. I have endeavoured
to treat the subject analytically rather than synthetically ^
because that race of successful experimental philosophers
— children — adopt this method.
For example, it is not by studying geometrical optics,
much less physical optics, that an infant gradually learns
to appreciate the distance of objects ; and later on it is
not by studying a treatise on struts, nor by listening to
a course of lectures on structures, that the child finds
out that the table has legs, hard legs, round legs. Feeling,
looking, trying, in fact a simple course of experimental
investigation, gives a child its knowledge ; and this, there-
fore, I venture to think, is the method we should adopt
when commencing the study of electricity.
The subject of current is treated first, because in
almost all the industries in which electricity is practi-
cally made use of, it is the electric current that is
employed ; secondly, because currents can be compared
with one another, and the unit of current (the ampere)
defined, without any knowledge of potential difference
or resistance. Potential difference is next considered,
and resistance the last of the three, because the very
idea of resistance implies a previous acquaintance with
the ideas of current and potential difference, since the
resistance of a conductor is the name given to the ratio
■of the potential difference (measured electrostatically) at
VI PRACTICAL KLECTIUCITY.
its terminals to the current passing through it. And it
was Ohm's experimental proof that this ratio was con-
stant for a given conductor at a constant temperature,
that led to resistance gradually coming to be considered
as a fixed definite property of a given conductor like its
weight or length."^
The legal unit of potential difference, however, tlie
volt, cannot be defined until the unit of resistance, the
ohm, has been considered, arising from the fact that,
whereas Ohm's law, as stated by himself, furnished us
with the meaning of an electrical resistance, and with
the meaning of one resistance being so many times
another, the Paris Electrical Congress started in their
definitions with the definition of the unit of resistance,
and used Ohm's law to give us the definition of a volt,
and the meaning of one potential difference being so
many times another. This rather complicates the logical
sequence in the mind of a beginner, and, to avoid the
difficulty to a certain extent, I have, in § 44, page 89,
taken a provisional electrostatic definition of a volt,
almost identical in value with the legal one, and super-
seded it by the legal one in § 81, page 141.
That a battery has a fixed E. M. F., has been deve-
loped from the laws of energy, and therefore, while
potential difference is treated before resistance, E. M. F.
is treated after.
The principles underlying the action of the electrc-
phorus, -and accumulating influence machines, such as
Thomson's replenisher, and the Wimshurst machine, are
considered late in the book, since the student can far
better understand the electrical action of these machines
when he has acquired clear ideas regarding capacity and
condensers.
In the tables, and generally throughout the book,
the legal units recommended by the Electrical Congress
of 1883 have alone been employed, since, although the
* The apparatus for proving this law experimentally, is depcribed
and illustrated on pages 134—136.
FKEFACU. VD
legal ohm is possibly 0*19 per cent, smaller than the true
ohm, it is very much nearer than the B. A. unit, which is
about 1*2 per cent, too small. Several examples, how-
ever, have been introduced to illustrate the mode of
converting results obtained by using the old units into
the numbers which would have been obtained had the
legal units been employed. The convenience of having
specific resistances, &c., expressed in legal ohms, and the
E. M. Fs. of important cells in legal volts, (fee, will be
apparent when I quote the resolutions passed last month
at the meeting of the British Association at Birmingham,
and which are given immediately after this Preface.
In working out the examples, Mr. Bottomley's very
useful book of logarithms has been used ; the answers,
therefore, only contain four significant iigures, the last
of which is only a[)proximately correct.
The expression difference of potentials, or even
potential difference, is a cumbersome one. The use of
the capital letters P. D. as an abbreviation for ])otential
difference, employed in the latter half of this book,
corresponding with the use of the letters E. M. F. for
electromotive force, may, I hope, find favour with the
Committee on Electrical Nomenclature. 1 have also,
throughout the book, used capital letters to stand for
currents, and small letters for resistances, as this dis-
tinction enables the equations and formulae to be much
more easily understood.
For the use of two or three of the figures I am
indebted to the kindness of Mr. Cunynghame, Mr. Gray,
and the Editors of the Electrician and Electrical Review.
With these exceptions, the illustrations are representa-
tions of the apparatus that has been devised by Mr.
Mather and myself for the first year's students at the
Fiiisbury Technical College and the Central Institution,
at both of which colleges it is in daily use. Hence, by
far the greater number of the figures have been drawn
for this book, and are not time-honoured representations
of historical apparatus.
Vlll PRACTICAL ELECTRICITY.
It will be observed that the apparatus required for
each experiment is mounted complete on a board. This is
to enable it to be easily carried backwards and forwards
between the laboratory and the lecture-room without
disarranging it. At first sight it might appear that the
student finding each set of apparatus joined up quite
complete, with current laid on allready for the carrying
out of the experiment, would prevent his learning to
adopt expedients for overcoming experimental difficul-
ties, and would retard his acquiring habits of originality.
For first year's students, however, I have found it a good
plan to have each set of apparatus complete in position ;
firstly, because it is only with some such arrangement
that fifty or more students can commence work almost
simultaneously, and in the course of two or three hours
have all performed some quantitative experiment ;
secondly, because when the apparatus is so arranged that
even beginners can perform several experiments success-
fully, they are less discouraged with the difficulties they
subsequently meet with when selecting and arranging the
apparatus for conducting some investigation, as they have
acquired faith in the possibility of success.
Here and there the apparatus is referred to as having
been devised by the author. In all such cases the word
author is to be taken in the plural sense, as my long
association with Professor Periy, and the interchange of
ideas that has taken place between us for the last eleven
years, render it quite impossible to distinguish to Avhich
of us the apparatus is due,
My cordial thanks are due to two of my assistants,
Mr. Mather and Mr, Raine, for correcting the proofs, and
making many valuable suggestions. I am also especially
indebted to the former for the very earnest, thoughtful, and
painstaking way in which he has for some years assisted
me in developing the course of instruction for students of
electrical technology, of which the present book represents
the elemeniary portion. ^ ^^ AYRTON.
October, 1886.
BRITISH ASSOCIATION FOR THE ADVANCE-
MENT OF SCIENCE.
September, 1886.
Sir, — At the Birmingham meeting of the British
Association, a meeting of the Committee on Electrical
Standards was held, and on the motion of Sir Wm.
Thomson, F.R.S., seconded by Prof. W. G. Adams,
F.R.S., it was agreed that the Committee should recom-
mend the British Government : —
(1) To adopt for a term of ten years the Legal Ohm
of the Paris Congress as a legalised standard sufficiently
near to the absolute Ohm for commercial purposes.
(2) That at the end of the ten years' period the Legal
Ohm should be defined to a closer approximation to the
absolute Ohm.
(3) That the resolutions of the Paris Congress with
respect to the Ampere, the Volt, the Coulomb, and the
Farad be adopted.
(4) That the Resistance Standards belonging to the
Committee of the British Association on Electrical
Standards now deposited at the Cavendish Laboratory at
Cambridge be accepted as the English Legal Standards
conformable to the adopted definition of the Paris Con-
gress.
T remain,
Your obedient servant,
R. T. GLAZEBROOK,
Secretary Electrical Standards Committee.
Cavendish Laboratory,
Cambridge.
TABLE OF CONTENTS.
CHAPTER 1.
THE ELECTRIC CUKllENT AND ITS MEASUREMENT.
HKCTION PAG*
1. What is meant by an Electric Current, and by its Direction
of Flow - - - 1
2. Properties of an Electric Current 3
3. Measuring the Strength of a Current •*
4. Conductors and Insulators 8
5. The Strength of an Electric Current : by which of its Pro-
perties shall it be Directly Measured ? - - - - 9
6. Definition of the Unit Current 11
7. Definition of the Direction of the Current - - - - 14
8. Objection to the Usual Mode of Constructing Voltameters - 18
9. Description of a Practical Form of Sulphuric Acid Volta-
meter 18
10. Relative Advantages of Voltameters and Galvanometers - 20
11. Meaning of the Relative and the Absolute Calibration of a
Galvanometer 22
11a. Measuring the Distribution of Magnetism in a Permanent
Magnet 24
12. Experiment for Calibrating a Galvanometer Relatively or
Absolutely 27
13. Graphically Recording the Results of an Experiment - - 30
14. Practical Value of Drawing Curves to Graphically Record
the Results of Exjieriments 33
CHAPTER II.
GALVANOMETERS.
15. Tangent Galvanometer 36
10. Scale for a Tangent Galvanometer 39
17. Mode of Making a Tangent Scale 39
18. Best Deflection to use with a Tangent Galvanometer - - 41
19. When the Tangent Law is True 41
20. Preceding Conditions are Fulfilled in the Tangent Galvano-
meter - - - - - 43
21. Adjusting the Coil of a Tangent Galvanometer - - - 46
22. Variation of the Sensibility of a Galvanometer, with the
number of Windings and with the Diameter of the
Bobbin 48
28. Thomson's Galvanometer for Large Currents - - - 53
CONTENTS. XI
SECTION PAGE
24. Values in Amperes of the Deflections of a Tangent Galvano-
meter controlled only by the Earth's Magnetism - - 54
25. Galvanometers having an Invariable Absolute Calibration - 57
26. Calibrating any Galvanometer by Direct Comparison with
a Tangent Galvanometer 58
27. Pivot and Fibre Suspensions 60
28. Sine Law : Under what Conditions it is True - - - 61
29. Preceding Conditions are Fulfilled in the Sine Galvanometer 62
30. Calibrating a Galvanometer by the Sine Method - - - 64
31. Calibration by the Sine Method of the Higher Parts of the
Scale 65
32. Calibration by the Sine Method with a Constant Current - 67
33. Method of Making a Sine Scale 68
34. Portable Galvanometer with Approximately Invariable Abso-
lute Calibration 69
35. Construction of Galvanometers in which the Angvdar Deflec-
tion is Proportional to the Current - - - - 71
36. Shielding Galvanometers from Extraneous Magnetic Dis-
turbance -. - - - -73
37. Direct-Reading Galvanometers 76
38. Advantages of the Previous Types of Galvanometers - • 78
39. Ammeter 79
CHAPTER III.
DIFFiillENCE OF POTENTIALS, ELECTRIC QUANTITY, DENSITY,
AND THEIR MEASUREMENT.
40. Difference of Potentials - ^ 80
41. Potential of the Earth Arbitrarily taken as Noiight - - 84
42. The Difference of Potentials between Two Conductors does
not Measure the Difference in their Electric Charges - 85
43. Volt - - - 86
44. IMeasuring Potential Difference by "Weighing - - - 88
45. Increasing the Sensibility of the Vfeight Electrometer by
using an Auxiliary High Potential 91
46. Rough Electrometer 94
47. Action of a Gold-leaf Electroscope 95
48. Objections to the Ordinary Methods of Constructing Gold-
leaf Electroscopes -96
49 Conduction and Induction 97
50. Potential Uniform at All Points Inside a Closed Conductor - 98
51. No Force Inside a Closed Conductor Due to Exterior Electri-
fication 99
52. A Metallic Box not a Magnetic Screen unless made of Very
Thick Iron 101
53. IMarine Galvanometer 103
54. Reflecting Galvanometers 103
55. Angular Slotion of the Reflected Ray is Twice the Angular
Motion of the Mirror - - 106
56. Connection between the Motion of the Image on a Plane
Scale and the Angular Deflection of the Mirror - - 107
Xll PRACTICAL ELECTRICITY.
SECTION FAOU
57. static Electrical Apparatus should be Enclosed in a Metallic
Case - - - . 108
58. Quantity of Electricity 109
59. Comparison of Quantities of Electricicy Ill
60. Quantity of Electricity produced by Rubbing Two Bodies
Together - - 113
61. Object of Rubbing Two Bodies Together to Produce Electri-
fication - - - 1.15
62. Proof-plane - - - 116
63. Electric Density 117
64. Density is Nought on the Inner Surface of a Closed Con-
ductor 118
65. Potential of a Conductor Depends Partly on the Amount of
Electricity on it 119
66. Potential of a Conductor Depends Partly on its Shape - - 119
67. Potential of a Conductor Depends Partly on its Position - 119
68. Modes of Varying the Potential of a Conductor - - - 121
69. Examples showing the Difference between Potential, Density,
and Quantity 121
70. Static and Current Methods of Measuring Potential Dif-
ferences Compared 125
71. When a Potential Difference Galvanometer may be Employed 127
72. Voltmeter 128
CHAPTER IV.
RESISTANCE AND ITS MEASUREMENT.
73. Resistance 129
74. Ohm's Law - - - - - - - - 130
75. Exjjerimental Proof of Ohm's Law 130
76. Comparing Resistances 136
77. Simple Substitution Method of Comparing Resistances • 138
78. Plug Key 139
79. Potential Difference Method of Comparing Resistances - 140
80. Ohm 140
81. Volt, Practical Definition of 141
82. British Association Unit of Resistance 141
83. Variation of Resistance with Length 143
84. Construction of Coils ; Multijiles of the Ohm - - - 145
85. Variation of Resistance with Sectional Area - - - - 146
86. Variation of Resistance with the Material . - - - 146
87. Variation of Resistance with Temperature . . - - 147
88. Construction of a Differential Galvanometer ■ - - 149
89. Construction of Plug Resistance Boxes 151
90. Law of the Variation of Resistance with Temperature - - 152
91. Resistance of Metals per Cubic Centimetre and per Cubic
Inch 153
92. Resistance of Metals for a given Length and Diameter, or
for a given Length and Weight 15«>
93. Comparison of Electric and Heat Conductivities - - - 158
CONTENTS. Xlll
BFCTION PAGE
94. Material Used in Eesistance Coils 159
95. Mode of Winding Resistance Coils 163
96. Calibrating a Galvanometer by Using Known Ilesistances - 164
97. Wheatstone's Bridge - - - - • - - - - 166
98. Superiority of the Wheatstone's Bridge over the Differential
Galvanometer, and Conditions affecting the Sensibility
of the Bridge 171
99. Commercial Form of Wheatstone's Bridge - - - - 172
100. Bridge Key 174
101. Use of a Shunt with the Bridge 176
102. Meaning of the Deflection on a Bridge Galvanometer - - 176
103. Shunts 177
104. Multiplying Power of a Shunt 178
105. Combined Resistance 178
106. Construction of a Shunt Box 181
107. Increase of the Total Current produced by the Employment
of a Shunt. — The Use of Shunts with a Differential
Galvanometer 183
108. Sliding Resistance Boxes 186
109. Measuring a Resistance during the Passage of a Strong
Current 187
110. Ohmmeter 190
111. Amount of Heat Generated by an Electric Current - - 192
112. Cooling Correction of the Observed Rise of Temperature
Curve ' - - - 196
113. Measuring a Current by the Rate of Production of Heat - 197
114. Work done in an Electric Circuit 199
115. Work done by a Current Generator. — Electromotive Force- 202
116. Variation of External Resistance, Current, and Potential
Difference at the Battery Terminals - - - - 204
CHAPTER V.
CURRENT GENEBATQRS.
117. Current Generators - - - 208
118. Batteries 209
119. DanieU'sCell 210
120. Minotto's Cell - - 211
121. Gravity Daniell 212
122. Chemical Action in the Daniell's Cell 215
123. Local Action 217
124. Grove's Cell 218
125. Bunsen's Cell 219
126. Leclanch^ CeU 220
127. Potash Bichromate Cell 222
128. Measuring the Electromotive Force of a Current Generator 224
129. INIeasuring the Resistances of Batteries .... 22.5-
1.30. P. D. 230
131. Comparing the Electromotive Forces of Batteries - - 231
132. Poggendorff's IMethod of Comparing Electromotive Forces - 234
XIV PRACTICAL ELECTRICITY.
SECTIOK rAQB
133. Electromotive Force of a Cell is Independent of its Size and
Shape " 236
134. Calibrating a Galvanometer by Employing Known Resist-
ances and a Cell of Constant E, M. F. - - - 238
135. Arrangements of Cells 239
130. Arrangement of a Given Number of Cells to produce the
Maximum Current through a Given External Resistance 243
137. Variation produced in the Total Current by Shunting a Por-
tion of the Circuit - 253
138. Constant Total Current Shvmts 2.57
139. Independence of the Currents in Various Circiiits in Parallel 260
CHAPTER VI.
INSULATION.
140. Surface Leakage, and Leakage through the ]\Iass - - - 266
141. Coating Insulating Stems with Paraffin Wax or Shell-I.ic
Varnish 267
142. Sealing up One End of a Cable when under Test - - 268
143. Construction of an Insulating Stand - - - . 268
144. Laws of Surface Leakage, and of Leakage through the Mass 270
145. Corrugating the Sides of Ebonite Pillars - - - . 272
146. Common Fault made in Constructing Ebonite Pillars - ■ - 272
147. Telegraph Insulators - - . - . . 274
148. Testing Insulators during Manufacture .... 275
149. Measuring High Resistances 277
150. Subdividing a P. D. into Known Fractions - - - - 278
151. Constant of a Galvanometer 278
152. Very Delicate Galvanometers 281
153. Thomson's Astatic Galvanometers 283
154. Importance of the Galvanometer being Well Insulated - 286
CHAPTER VII.
QUANTITY AND CAPACITY.
155. Coulomb 289
156. Ballistic Galvanometer 292
157. Correction for Damping 296
158. Logarithmic Decrement 296
159. Determining the Logarithmic Decrement when the Damping
is Very Slight 297
160. Comparing Quantities of Electricity 299
161. Capacity 300
162. Condenser 301
163. Capacity of a Condenser is Constant - - - - - 302
164. Variation of the Capacity of a Condenser with the Area of
its Coatings 303
165. Variation of the Capacity of a Condensor with the Distance
between the Coatings - - 303
166. Farad 307
CONTENTS. X.V
BTCTlOy FAGB
167. Charge in Terms of Capacity 308
168. Capacity of a Cylindrical Condenser .... 308
169. Specific Inductive Capacity 309
170. Condensers for Large P. Ds. 313
171. LeydenJar - - 314
172. Battery of Leyden Jars 317
173. Constructing Condensers of Very Large Capacity - - 317
174. Comparing Capacities :>19
175. Charge and Discharge Key 320
176. Condensers are Stores of Electric Energj', not of Electricity 322
177. Absolute Measurement of a Capacity 327
178. Statical Method of Comparing Capacities ... - 330
179. Measuring Specific Inductive Capacity .... 332
180. Standard Air Condenser 334
181. Every Charged Body forms One Coating of a Condenser - 338
182. Capacity of a Spherical Condenser 338
183. Condenser Method of Comparing the E. M. Fs. of Current
Generators 341
184. Condenser Method of Measuring the Res'stance of a Cur-
rent Generator 342
185. Measuring a Resistance by the Rate of Loss of Charge - 344
186. Rate of Loss of Charge from Leakage through the Mass
depends on the Nature of the Dielectric only, and not
on the Shape or Size of the Condenser - - - - 346
187. Galvanometric Method of Measuring Resistance by Loss of
Charge 348
188. Multiplying Power of a Shunt used in Measuring a Discharge 349
189. Production of Large Potential Differences - - - - 351
190. Condensing Electroscope - - 352
191. Calibrating a Gold-Leaf Electroscope 354
192. Electrophorus 356
193. Ebonite Electrophorus arranged to give Negative Charges - 359
194. Accumulating Influence Machines 361
195. Thomson's Replenisher 364
196. Wimshurst Influence Machine 367
197. Dry Pile 372
CHAPTER VIII.
COMMEllCIAL AMMKTERS AND VOLTMETERS.
198. Defect of Permanent Magnet Meters 37S
199. Siemens' Electro-Dynamometer 377
200. Cunynghame's Ammeter and Voltmeter .... 382
201. Instruments with Magnifying Gearing 386
202. Magnifying Spring Ammeter and Voltmeter - - - 386
203. Gravity Control Meters 391
204. Crompton and Kapp's Meters 392
205. Paterson and Cooper's Electro -magnetic Control Meters - 393
206. Testing Ammeters -------- 394
207. Test for Accuracy of the Graduation - - - - - 395
208. Test for Residual INIagnetism 400
x\^ PRACTICAL elp:ctricity.
SECTION PAOE
209. Test for Error on Reversing the Current .... 402
210. Test for Error Produced by External Macinetic Disturbance 403
211. Test for Permanent Alteration of Sensibility - . . 407
212. Testing Voltmeters 407
213. Test for Accuracy of the Graduation 408
214. Latimer Clark's Cell 410
215. Standard Daniell's Cell 411
216. Test for Heating Error - 415
217. Variation of the Sensibility of a Galvanometer with its
Resistance 416
218. Rate of Production of Heat in Galvanometer Coils - - 419
219. Standard Voltmeter 422
220. Cardew's Voltmeter 423
221. Commutator Ammeter and Voltmeter - - - - 427
222. Calibrating a Commutator Ammeter 432
223. Calibrating a Commutator Voltmeter - - - • 433
224. Best Resistance to give to a Galvanometer - - - - 435
CHAPTER IX.
rOWER AND ITS MEASUREMENT.
225. Power 441
226. Watt 442
227. Wattmeter 444
228. Distribution of Power in a Circuit 445
229. Current that Develoj)s the Maximum Useful Power • - 448
230. Efficiency 451
231. Measuring the Efficiency of an Electric Light - - - 452
232. Dispersion Photometer 454
233. Efficiency and Life of Incandescent Lami)s ... - 458
Appendix to the Section on Shunts.
234. Kirchhoff' s First Law 464
235. Kirchhoff 's Second Law 464
236. Current through the Galvanometer of a Wheatstone's
Bridge 465
237. Best Resistance for the Galvanometer with a Wheatstone's
Bridge 466
238. Best Arrangement of the Battery and Galvanometer with a
Wheatstone's liridge 467
239. Measuring a Resistance containing an E. M. F. - - - 469
Specimens oe Instructions for Experiments.
To compare the amount of Chemical Decomposition produced
per second by a current with the corresponding Defec-
tion of a Tangent Galvanometer 476
Experiments on Shunts 478
To Calibrate an Ammeter by the Calorimetric Method - - 480
To Calibrate an Ammeter by means of a Silver Voltameter - 482
Practical Electricity.
CHAPTER I.
THE ELECTRIC CURRENT AND ITS MEASUREMENT,
1. What is meant by an Electric Current, and by its Direction of Flow
— 2. Properties of an Electric Current — 3. Measuring the Strength
of a Current— 4. Conductors and Insulators — 5. The Strength of
an Electric Current : by which of its Properties shall it be
Directly Measured? — 6. Definition of the Unit Current — 7.
Definition of the Direction of the Current — 8. Objection to the
Usual Mode of Constructing Voltameters— 9. Description of a
Practical form of Sulphuric Acid Voltameter — 10. Kelative Ad-
vantages of Voltameters and Galvanometers — 11. Meaning of the
Relative and the Absolute Calibration of a Galvanometer — 11a.
Measuring the Distribution of Magnetism in a Permanent Magnet
— 12. Experiment for Calibrating a Galvanometer Relatively or
Absolutely — 13. Graphically Recording the Results of an Experi-
ment— 14. Practical Value of Drawing Curves to Graphically
Record the Results of Experiments.
1. What is meant by an Electric Current, and by its
Direction of Flow. — In the various industries in which
electricity is employed, as in the telegraph, telephone,
electric lighting, electrotyping, electroplating, torpedo
exploding, and in the working of machinery by the aid
of electromotors, it is the so-called " electric current " that
is made use of. Hence a knowledge of the laws of this
electric current, a clear conception of its so-called proper-
ties, combined with a practical acquaintance with the
modes of measuiing it, must be of especial importance for
a right understanding of the working of the apparatus
employed in the above-mentioned industries. Indeed,
such knowledge is absolutely necessary if the user of
electrical apparatus is desirous of employing it to the
best advantage, of being able to correct faults when they
6
2 PRACTICAL ELECTRICITY. [Chap. L
occur, as well as of eflfecting improvements in the instru-
ments themselves.
It is customary to speak of an electric current as
if it had an independent existence apart from the
" conductor^' through which it is said to be flowing, just
as a current of water is correctly spoken of as something
quite distinct from the pipe through which it flows. But
in reality we are sure neither of the direction of flow of
an electric current, nor whether there is any motion of
anything at all. And the student must not assume that
the conventional expression, — the current flows from, the
copper pole of a galvanic battery to the zinc pole through
the external circuit, — implies any knowledge of the real
direction of flow any more than the railway expressions,
" up train " and " down train," mean that either train is
necessarily going to a higher level than the other. In
the case of a stream of water flowing along a river-bed
we are quite certain that there is water in motion, and
every one is agreed as to which way the water is flow-
ing; a cork or a piece of wood thrown on the water
indicates by its motion the direction in which the water
is moving.
Nor, again, must an electric current be supposed
to be like waves of sound travelling along, sinoe in this
latter case, although there is no actual travelling along of
matter, still the direction of motion of the wave of sound
is perfectly definite. Indeed, a wire along which an
electric current is flowing is more like a wire at each end
of which a nmsical instrument is being played, so that
the sound is travelling in both directions along the wire
at the same time. In short, the statement that an electric
current is flowing along a wire is only a short way of ex-
pressing the fact that the wire and the space around the
wire are in a diflerent state from that in which they are
when no electric current is said to be flowing. So that
when a body and the space around the body possess certain
properties that they do not usually possess, an electric
current is said to be flowing through that body.
Chap. I.J PROPERTIES OP AN ELECTRIC CURRENT. 3
2. Properties of an Electric Current. — These pro-
perties are :
(1) A suspended magnet put in nearly any position
near a body through which an electric current is said to
be flowing will be deflected, also a piece of iron put near
this body will become magnetised, the action in both
cases being produced as if the body conveying the current
had become magnetic.
(2) If the circuit through which the electric current
is said to bfe flowing be partly solid and partly liquid, then
the liquid will generally be decomposed into two parts,
one part going to one side of the liquid in the direction in
which the current may be said to be flowing, and the
other part going to the other side of the liquid in the
opposite direction to the flow of the current.
(3) The body conveying the current becomes more or
less heated.
In popular language the current is said :
(1) To deflect the magnet^ and magnetise the i/ron.
(2) To decompose the liquid.
(3) To heat the body through which it isflounng.
But as we have no evidence of the current apart from
the conductor through which it is said to flow, it is more
accurate to say, that when these effects are found to be
produced, a current is said to be flowing through the
conductor ; than to say, that the current produces these
effects. The latter expression, however, for brevity's
sake, is generally adopted ; and, indeed, the heat generated
in a wire conveying a current has so many analogies with
the heat produced in a pipe by the friction of a stream
of water passing through it, that we can frequently
assist ourselves by thinking of an electric current as a
stream of matter passing through the wire as water would
pass through a pipe filled with sponge or loosely packed
with sand. But the analogy, like many other analogies,
must not be pressed too far, especially as there is this
very great difference between a current of water flowing
in a pipe and a current of electricity in a wire, viz., that
4 PRACrriCAL electricity. [Chap.1
in the former case no effects are produced external to the
pipe, whereas in the latter the whole space surrounding
the wire is affected.
The magnetic, chemical, and heating effects of a current
are utilised practically in a number of electrical instru-
ments ; for instance :
Magnetic Property — Needle telegraph, the Morse in-
strument, electric bells, arc lamps, dynamo machines,
electromotors, and, in fact, all instruments using electro-
magnets.
Chemical Property — Electroplating, electrotyping, the
cleansing of the mercury used in the extraction of gold
from sand, &c.
Heating Property. — Electric lamps, contrivances for
lighting gas or oil lamps electrically, fuses for tor-
pedoes, &c.
The heating effect of the current is, as we shall see,
the effect which always occurs when a current flows ; that
is to say, it is impossible for a current to flow through
a body without some heat being produced ; and not only
is heat produced by the ordinary currents flowing through
telegraph wires, and which are sometimes not much more
than three-thousandths of the strength of the current flow-
ing through an incandescent lamp, but even the currents
used with the Bell telephone worked without a battery
produce a definite amount of heat in a given telephone
circuit, even though such telephone currents are very
weak compared with the currents used in telegraphy.
The actual measurement of the heat, however, would be
extremely difficult, if not impossible, to carry out with
existing apparatus.
3. Measuring the Strength of a Current. — As,
then, the production of heat always accompanies the
passage of a current, it might seem that the amount of
heat produced in a given time ought to be taken as a
measure of the strength of the current. But, in addition
to the difficulty of measuring the small amount of heat
produced by weak currents, the only way we have of
Chap. I.] MEASURING 1?HE STRENGTH OF A CURRENT.
6 PRACTICAL ELECTRICITY. [Chap. I.
measuring the amount of heat given to a body is an indirect
one, and consists in measuring its rise of temperature by
means of a thermometer. But as a thermometer measures
merely rise of temperature, and not the amount of heat,
and Sis the rise of temperature of a body through which a
curi'ent is passing can, without varying the current, be
varied, by increasing or diminishing the facility that the
body may have for cooling, various precautions have to
be adopted, and further experiments have generally to
be made to enable us to deduce from the observed rise
of temperature the real amount of heat that was given
to the body.
In order to ascertain which of the properties of a cur-
rent can be best employed for measuring its strength,
an experiment may be made with the following ap-
paratus : —
A, B, c, D, E (Fig. 1) are instruments so arranged
that the same electric current will be sent through
them all by the battery b 6, on joining the wires P and Q.
A is a coil of cotton- or silk-covered wire, with a magnet m
suspended so as to turn freely inside the coil, the whole
arrangement forming what is called a '' galvanoscope"
B is an "electromagnet" consisting of a coil of cotton- or
silk-covered wire wound in opposite directions round the
ends of a piece of iron of horse-shoe form, c is a " sul-
phuric acid voltameter " consisting of two platinum plates
dipping into moderately dilute sulphuric acid in a vessel v,
closed by an air-tight stopper s, through which passes a
glass tube t, open at both ends, and with its lower end
nearly touching the bottom of v. This tube is graduated
in fractions of a cubic inch. d consists of two thin
copper plates p,py dipping into a solution of copper
sulphate (the blue vitriol of commerce), and is called a
" copper voltameter." e is a coil of bare wire immersed
in paraffin oil, the temperature of which can be measured
by the thermometer t, the arrangement being called a
" calorimeter"
Connect the two wires p and q, and allow the current
Chap. 1.] MEASURING THE STRENGTH OF A CURRENT. 7
to pass for a convenient time through these five pieces of
apparatus, then it will be found that :
1st. The liquid has risen a distance di in the tube t
of the voltameter c, indicating that the passing of the
current through the liquid from one of the platinum
plates to the other has caused c^ cubic inches of gas to be
generated.
2nd. One of the plates in the copper voltameter has
increased in weight by w^ grains.
3rd. The mercuiy in the thermometer t of the calori-
meter E has risen through t>°.
4th. The magnetic needle m of the galvanoscope a has
all the time been kept dedected from its original position
through a number of degrees n°.
5th. If at any time during the passage of the current
the armature a was placed carefully on the ends of the
horse-shoe electromagnet b it required a pull of w^ lbs., as
measured by the spring balance, to pull it off, when the
handle at the top of the apparatus was slowly turned.
Next increase the strength of the current passing
through the apparatus c, d, e, a, b, by increasing the num-
ber of cells forming the battery 6 6 or in any other way,
such as will be described later on, then each of the effects
previously observed with these instruments will be in-
creased, and instead of the results Cj, Wj, d^°, Ni°, w^j we
shall obtain c^, Wg, Dg^, n.°, w.^. But it will be found that
the new values do not all bear the same ratio to the corre-
sponding old ones. For example, if c^ is twice Cj, then No°
may be more or less than twice Ni°, but will generally be
less than twice, while D2° and W2 will be found to be much
greater than twice 1)° and w^ respectively. On the other
hand, if the strength of the second current be so chosen
as to make 03° exactly twice Dj°, then generally it will be
found that W2 is rather more than twice Wi, while Cg and
W2 are much less than twice Cj and w^ resjDectively.
If, then, we arbitrarily define the strength of the
current as being directly proportional to the gas evolved
in the sulphuric acid voltameter, we must conclude
d PRACTICAL ELECTRICItY. (Chap. L
that if Cj is exactly double c^ we have doubled the cur-
rent strength ; but, on the other hand, if we prefer to
say that strength of current is directly proportional to
the angular deflection of the needle m in the galvano-
scope A, then we must conclude that, as Ng" is less
than twice Ni°, we have not quite doubled the strength
of the current; whereas if we prefer to say that cur-
rent strength shall be regarded as proportional to the
force required to detach the armature a of the electro-
magnet B, or, instead, proportional to the rise of tem-
perature of the liquid in the calorimeter e iii a given-
time, then we must conclude that the strength of the
current has been much more than doubled. Which of
these is right and which wrong ? As long as no one of
the effects varies we may be safe in concluding that the
strength of the current is constant, but if the different
effects to which we have been referring vary from one
time to another, then which of them shall we take to
represent by the magnitude of its variations the change
that has taken place in the current strength 1
In the case of measuring the velocity of a stream of
water, or the number of gallons of water per minute dis-
charged by a river, no two experimenters could differ. One
of them, of course, by the employment of better con-
structed measuring instruments, or it may be from having
greater experience in making such measurements, might
get answers slightly different from, and more accurate
than, those obtained by the other experimenter. But they
could not have such totally different conceptions of what
should be meant by the velocity of theVater in a particular
part of the channel, or of the total discharge, in gallons
per minute, that the results obtained by one observer were,
apart from all mere errors of experiments, twice as great
as those obtained by the other. And this is because they
would be dealing with the actual flow of a material sub-
stance— water.
4. Conductors and Insulators. — The various pieces
of apparatus in Fig. 1 are joined by bits of copper wire,
Chap. 1.] CONDUCTORS AND INSULATORS. 9
but as long as there is even one break in the continuity,
as at PQ, no current can be sent by the battery hh
through the circuit, because the air separating the wire p
from the wire Q " insulates " or is an " insulator." If p
be pressed against Q, but with a thin piece of paper,
or silk, or indiarubber, &c., between, still no current
will flow, because all these substances are more or less
good insulators. If, however, the ends <S£ the wires p
and Q be rubbed clean with emery paper^ or be scraped
clean with the back of a knife or a file, and then pressed
together, the current will flow, since there is good " con-
ductivity " or little " resistance " between the clean sur-
faces of metals pressed together.
5. The Strength of an Electric Current : by which
of its Properties shall it be Directly Measured ? —
To assist us in deciding whether the amount of the
magnetic action, or of the chemical action, or the amount
of heat produced in a given time shall be arbitrarily
taken to be that magnitude to which the current strength
shall be defined as being directly proportional, we may
observe that if the five pieces of apparatus A, b, c, d, e em-
ployed in the previous experiment be selected without
special reference to their sizes and shapes, Cg and Wg will
be found to be the only two out of the five quantities that
bear the same ratio to their respective previous values.
And in both the voltameters it was chemical decompo-
sition that took place ; in the former, this decomposition
being the splitting up of the liquid into gases ; in the latter,
the splitting up of the copper sulphate^ and the deposit of
copper on one of the copper plates, together with an
eating away of the other copper plate to give back to the
copper sulphate solution the amount of copper taken out
of it.
In A and b the effects produced are both magnetic,
but it will not be found that Ng" bears to N° the same
ratio that W2 bears to w^. Consequently, as far as we
have seen at present, the amount of chemical action pro-
duced in a given time by a current appears to be a more
10 PRACTICAL ELECTRICITY. [Chap. I.
direct measure of its strength than the magnitude of the
magnetic effect produced.
To examine this point still further, let us have two
sulphuric acid voltameters of totally different shapes and
sizes, two copper voltameters also of different shapes and
sizes, the copper plates, for example, being much larger
and either much nearer together or much farther apart in
the one than in the other, also two galvanoscopes, two
electromagnets, and two calorimeters, the two instru-
ments in each case being selected so as to be distinctly-
different in size and form. Then in sending the same
current through them all, the following results will
be observed : In the two sulphuric acid voltameters quan-
tities of gas equal in mass, and therefore occupying the
same volume at the same pressure and temperature, will
be developed in the same time, in spite of the platinum
plates being of a very different size and at a very different
distance apart in the two voltameters.* Similarly, in
spite of the difference in size and form in the two copper
voltameters, the increase in weight of the plate of the one
will be exactly the same as the increase in weight of the
corresponding plate of the other, f But in the case
of the two galvanoscopes, the two electromagnets,
and the two calorimeters, although the same current is
passing through them, the effects depend on the shape,
on the size, and on very many details in the arrange-
* Equality of pressure may be obtained by using for the volta-
meters two vessels of the same size as well as two tubes of the same
bore, and filling the vessels with the same quantity of dilute sulphuric
acid of the same specific gravity. In that case, if the level of the liquid
in the two tubes be the same to start with, the liquids will be found
to rise at exactly the same rate in them on the same current being sent
through the two voltameters.
t If the plates in one of the voltameters be very small, the
copper deposited may drop to the bottom of the vessel, instead
of adhering to the plate. In measiiring the increase of weight of
the plate this copper at the bottom of the vessel must be collected
and weighed. In making the experiment, however, it is better, at
any rate, in the first instance, to use, in both copper voltameters, plates
sufficiently large for all the copper that is deposited to adhere Jirmly
to the plates. {See the second note on page ll.)
Chap. I.] THE UNIT CURRENT: THE AMPERB. 11
ment, &c. Hence, to specify the strength of a current by
the magnitude of the deflection of the needle of a gal vano-.
scope, it would be necessary to state the exact mode of con-
structing each part of the galvanoscope in great detail, as
well as the exact position of the instrument relatively
to neighbouring magnetic pieces of iron. Whereas, to
specify the strength of a current by the amount of gas
produced in a given time in a sulphuric acid voltameter,
or by the amount of copper deposited in a given time on
one of the plates of a copper voltameter, neither the
shape nor size of the plates, nor the distance between
them, need be taken into account within wide limits.
6. Definition of the Unit Current. — We shall,
therefore, define the strength of a current as being
directly proportioned to the amount of chemical decompo-
sition produced in a given time; and the current that
deposits 0*00111815 gramme, or 0-017253 grain, of silver
per second on one of the plates of a silver voltameter, the
liquid employed being a solution of silver nitrate, con-
taining from 15 to 30 per cent, of the salt, we shall call
an " ampere, ^^ and take it as our unit current.*
The same current is found to deposit 0*00032959
gramme, or 0-005084 grain, of copper per second on one
of the plates of a copper voltameter,! and 0-0003392
* The silver is usually deposited on the inside of a light platinum
bowl, and Lord Rayleigh finds that if a fairly strong solution be em-
ployed, and the deposition be not continued for more than a quarter of
an hour, a uniform adherent deposit of silver will be obtained if the
current does not exceed about one ampere per six square inches ; that
is to say, if not more than about three-thousandths of a gi'ain of silver
be deposited per second on a square inch of the surface of the platinum
bowl. The other pole should consist of a silver disc placed horizontally,
and wrapped in filteiing paper to prevent particles of oxide of silver
which may become detached from the silver plate dropping on to the
platinum, and making the weight appear to be too great. The edge of
the silver disc should be about eqiii-distant from the side and the
bottom of the bowl. {See § 207, page 395.)
t In order that a current may be measured accurately in amperes
with a copper voltameter, Dr. Hammerl finds that the plates may be
conveniently put at about half an inch from one another. If put too
near, what is called *' polarisation " will occur if the current to be
measured is strong, and it Avill be difficult to keep it constant in
12 PRACTICAL ELECTRICITY. [Cbap. I.
gramme, or 0*005232 grain, of zinc per second on one of
the plates of a zinc voltameter,^ and also to decompose
0-00009326 gramme, or 0-001439 grain, of dilute sul-
phuric acid per second. The acid in the sulphuric acid
voltameter may be conveniently diluted with water until
the specific gravity of the mixture is about I'l, which
corresponds with about 15 per cent, by weight of pure
sulphuric acid at 15° 0.
The volume of mixed gas (oxygen and hydrogen) that
is produced per second -by the decomposition corres-
ponding with a current of one ampere equals in cubic
centimetres
0-1738 X 76 (273 + C.°)
A X 273
where C.° is the temperature of the mixed gas in degrees
Centigrade, and h the pressure in centimetres of mercury.
If the volume be measured in cubic inches, the tem-
perature in degrees Fahrenheit, and the pressure in inches
of mercury, the formula becomes
0-01058 X 30 (491 -f- F.°-32°)
h X 491
Example 1. — How many amperes would deposit 5
grammes of copper in half an hour, the current being
supposed constant?
strength. The plates should be as square as i^ossible, and in order
that the deposit of copper should adhere well to the plate, the surface
of each of the two plates immersed in the copper sulphate solution,
should be at least two square inches for each ampere of current to be
measured, this area being reckoned only on the sides of the plates op-
posed to one another. The plate on which the copper is deposited,
and which is the only one that need be weighed, should be made of
hard thin copper, so as to be as light as possible for its area, in order
that the weight of the film of copper deposited on it may be accurately
determined.
* The chemical equivalents here employed in calculating the
weights of copper and zinc deposited per second by an ampere from the
weight of silver deposited by that current are : silver, 107 "66 ; copper,
63-47 ; zinc, 65-33.
Chap. 1.1 EXAMPLES. 13
0*0003295 grammes are deposited in 1 second by 1 ampere.
. • . 6 grammes are deposited in 1 second by
5 grammes are deposited in 30 x 60 seconds by
5
0-00032i>5 X 30 X 60 ^'^P®''^"'
Answer. — 8-430 amperes.
Exaw/ple 2. — How many grammes of copper would
be deposited by a steady current of 40 amperes acting
for 5 hours %
1 ampere acting for 1 second deposits 0-0003295 grammes.
40 amperes acting for 60 x 60 x 5 seconds
deposit 0-0003295 x 40 x 60 x 60 x 5 grammes.
Answer. — 237*24 grammes.
Example 3. — How many amperes would deposit 9
grammes of copper in 2^ hours, the current being con-
stant? Answer. — 3*035 amperes.
Example 4. — How many grammes of copper would
be deposited by a steady current of 1*5 amperes acting
for 16 seconds? Answer. — 0*007908 grammes.
Example 5. — How many grammes of sulphuric acid
would be decomposed by a steady current of 12 amperes
acting for one hour ? Answer. — 4*028 grammes.
Example 6. — How many amperes would deposit 18
grammes of zinc in If hour, the current being con-
stant? Answer. — 8*428 amperes.
Exam,ple 7. — If the mixed gas produced in a sul-
phuric acid voltameter be at 20° C, and the barometer
stand at 77*5 centimetres, what volume of gas would be
produced in half a minute by a stead;^^m:rent of 18
amperes ? ^^t^ -i^^
14 PRACTICAL ELECTRICITY. [Chap. L
cubic centimetres of gas.
6
cubic centimetres of gas.
1 ampere in 1 second produces
0-1738 X 76 X (273 + 20)
77-5x273
18 amperes in 30 seconds produce
0-1738x76x293x18x30
77-5 X 273
Answer. — 98*77 cubic centimetres of gas.
Exami:>ie 8. — If the temperature of the mixed gas in
a sulphuric acid voltameter be 19°-5C., and the height
of the barometer 75 centimetres, what current would pro-
duce 50 cubic centimetres of mixed gas in one minute ?
Answer. — 4-418 amperes.
7. Definition of the Direction of the Current. —
The next thing to define is the direction of the current,
which, as already explained, can only be done in a conven-
tional way. In the case of a sulphuric acid voltameter
we have hitherto only spoken of the total quantity of gas
given off at both platinum plates, but if these gases be col-
lected in separate tubes, as can very conveniently be
done in the Hoflfmann's voltameter (Fig. 2), then it is
found that at one of the plates p oxygen gas is given off,
and at the other p hydrogen, exactly in the proportions
in which these two gases have to be combined together to
form water ; viz., two volumes of hydrogen and one of
oxygen.* So that the " electrolytic " action effected by
sending a current from one platinum plate to another
in dilute sulphuric acid, is exactly the same as if the
water had simply been decomposed. That sulphuric
acid must be added to distilled water in order that an
electric current may flow through it and produce oxygen
and hydrogen, may easily be shown experimentally, but
we are not sure of the exact action of the sulphuric
acid ; it may be that the sulphuric acid has to be added
* That the gases are hydrogen and oxygen can be proved by the fact
that on turning the stop-cocks s, s,the one H when lighted will burn with
a pale blue flame, and the other o will ignite a glowing piece of wood.
Chap. I.]
DIRECTION OF A CURRENT.
15
merely to make the non-conducting distilled water more
conducting in order that it may become possible to send
a strong current through the mixture with ordinary bat-
teries ; or it may be that it is the
sulphuric acid that is decomposed
by the current, and that the water
is decomposed by a secondary
chemical action. In the latter
case the action would be repre-
sented in chemical symbols as
follows :
Electrical decomposition
H2SO, = Ho + S04.
Subsequent chemical action
HgO + SO^rrrHgSO^ + O.
Whichever may be the true ex"
planation, the effect of the ^^ electro'
lysis " of dilute sulphuric acid is
that two volumes of hydrogen
come off at one platinum plate
and one volume of oxygen at the
other, and the current is said to
travel through the liquid towards
the plate at which the hydrogen
is given off, or the current flows
through the liquid loith the hydro-
geriy so that in the Hoffmann's vol-
tameter, shown in Fig. 2, the cur-
rent would be said to flow through
the liquid, in the short horizontal
tube, from right to left.
If an acid, a copper, and a zinc voltameter be all
joined together, so that the same current passes through
them, then it will be found that the hydrogen in the first,
the copper in the second, and the zinc in the third, all
travel in the same direction, so that if through the liquid
in an acid voltameter the cmrrent be said to go in the
Fig. 2.
16
PRACTICAL ELECTRICITY.
[Chap. I,
direction in which the hydrogen travels, then through the
liquids in a copper and in a zinc voltameter, it must be
said to go in the direction in which the copper and the
zinc travel. With this definition of direction of current
rig. 3.
we find that if a compass needle be placed under a tele-
graph wire running north and south, the north-seeking *
* The '^north-seeking" end of a magnet is the one that points
towards the geographical north. The simple expression " north" end
is confusing, since in England it refers generally to the end of a mag-
net that points to the north, while in France it refers to the end that
points to the south, th-e French using that definition because that end
18 attracted by the earth's magnetism situated in the southerQ
Chap. I.J
DIRECTION OF A CURRENT.
17
end of the compass
needle is deflected to-
wards the east when
the current is flowing
along the telegraph
wire from north to
south.
Or, again, if a
wire conveying a cur-
rent be coiled round
a piece of iron shown
end-on to an observer,
then the end of the
iron nem^est him will
act as the nortJi-seekhig
end of a mag'net when
tJie current ajipears to
the observer to flow
round the wire in the
direction opposite to
that in which the
hands of a clock go {or
simply contra - clock -
loise). If the observer
now look at the other
end of the bar, he
will, of course, see
the south-seeking end,
and in his new posi-
tion the cuiTent will
now appear to him to
flow round the wire
hemisijhere, and the unlike ends attract one another. Calling the ends
of magnets ''red" and ''blue'' is equally confusing, as some people
use one of these two colours, and others the other colour, to stand
for the same end. As, however, the north-seeking end of a magnet is
usually marked by instrument makers with a scratch or a cut, it would
probably be best to call the north-seeking and south-seeking ends of a
magnet the ''marked end " and " unmarked end " respectively.
C
J 8 PRACTICAL ELECTRICITY. [Chap- 1
in the same direction as that in which the hands of a
clock go (or clockwise). The relative magnetic polarity
of the iron bar and the direction of the current, as
indicated by the arrows, are shown in Fig. 3.
Perhaps the simplest method for remembering the con-
nection between the magnetic polarity of an iron bar and
the direction in which a current circulates round it is,
that ii a current circulates round the bar in the direction
in which the iron of the thread of a corkscrew (Fig. 4)
movesi when the corkscrew is screwed down or up, the
point of the ' screw will move towards the north-seeking
magn<3tic end of the iron bar.
8. Objection to the .Usual Mode of Constructing
Voltameters. — The sulphuric acid voltameters, as usually
pictured in books, and which are the forms obtainable at
shops, are extremely unsuitable for practical use, as it is
troublesome, after the tubes in which the gas is collected
are full of gas, to fill them with liquid again for a new ex-
periment. The apparatus shown in Fig. 2 is very con-
venient when it is required to collect the oxygen and
hydrogen separately, but it has the inconvenience that,
the platinum plates being small and far apart, it requires
the employment of several galvanic cells to make the gas
come off quickly ; for although the quantity of- gas pro-
duced in a given time by the same current is independent
of the shape and size of the plates, the ease with which
this current can be generated depends very materially on
the size of the plates and their distance apart, and if we
wish to produce chemical decomposition quickly, we
ought to have the plates large and very near together,
and the liquid employed ought to contain something like
33 per cent, of strong sulphuric acid by weight, the mix-
ture having a specific gravity of about 1*25 at 15° 0.
9. Description of a Practical Form of Sulphuric
Acid Voltameter. — In Fig. 5 is shown a very convenient
form of voltameter, designed by the author, consisting
of a glass vessel closed at the top with an indiarubber
stopper I, and containing moderately dilute sulphuric
Chap. I.]
SULPHURIC ACID VOLTAMETER.
19
acid. The two platinum plates p are held together by
indiarubber bands, but prevented from touching one
another by small pieces of glass tubing put between the
plates at the top and bottom. Wires coated with gutta-
percha, to prevent their being corroded by acid being
spilt over them, go from the plates, one to the '^ key" K,
which is raised up above the general level of the appa-
ratus also to prevent its being corroded by
drops of acid, and the other wire to one of
the terminal binding screws seen in the figure.
On pressing down k, the current produced
by a generator attached by wires to the two
binding screws, seen
at the right-hand side
of the figure, is allowed
to pass through the
apparatus. The gra-
duated tube tj which
passes air - tight
through the india-
rubber stopper, and
reaches nearly to the
bottom of the vessel,
terminates at the up-
per end in a thistle
funnel, so that if the
current is by accident
kept on for a longer time than is necessary to cause the
liquid to rise to the top of the graduated tube, the liquid
collects in the funnel instead of spilling over. This tube
is also sloped so that the rise of liquid in the tube may
increase the pressure of the gas in the upper part of the
voltameter as little as possible.* The second tube might
be simply terminated with a piece of indiarubber tubmo-
o
* If the vessel be full of liquid so that there is no gas between
the top of the liquid and the indiarubber stopper F at the commence-
ment of the experiment, the error arising from the compression of the
gas produced by the rise of liquid in the tube t may be neglected
Fig. 5.
. 20 PRACTICAL ELECTRICITY. [Chap. I.
closed with a pinch-cock, on opening which the gas is
allowed to escape, and the liquid runs back out of the
tube t If this is done suddenly, however, there is a
tendency for small particles of the liquid to be jerked out
of tbe lower tube. To prevent these particles being thrown
on to the stand of the apparatus, the tube is carried up,
and its cord is bent over into the thistle funnel.
10. Relative Advantages of Voltameters and Gal-
vanometers.— The disadvantage of employing a voltameter
for the practical measurement of currents is, that it re-
quires a strong current to produce any visible* decompo-
sition in a reasonable time. Even the current of one
ampere, which is about that used in an ordinary Swan
incandescent lamp, would require two hours, fifty -eight
minutes, and forty-five seconds to decompose one gramme
of dilute sulphuric acid, whereas the weak curi'ents used
in telegraphy, and, still more, the far weaker currents
used in testing the insulating character of specimens of
guttapercha, indiarubber, &c., might pass for many days
through a sulphuric acid voltameter before their presence
could be detected, much less their strength measured.
Indeed, not to mention the enormous waste of time, and
the difficulty of keeping the current strength which it was
desired to measure constant all this time, the leakage of
the gas which would take place at all parts of the appa-
ratus that were not hermetically sealed,* would render
such a mode of testing quite futile. Hence, although the
voltametric method is the most direct way of measuring
a current strength, and although it is constantly made
use of for measuring th« large currents now used indus-
trially, still the very fact that the amount of chemical
decomposition produced in a given time by a certain
current is independent of the shape or size of the instru-
ment, makes it impossible to increase its sensibility.
* A glass vessel is said to be hermetically sealed when any opening
that previously existed in it has been closed, by heating the glass round
th-e opening until it becomes soft and sticky, and pressing the edges
together.
Chap. I.] GALVANOMETERS AND VOLTAMETERS. 21
Consequently some other apparatus must be employed for
practically measuring small curi'ents, and the law of the
apparatus, that is, the connection between the real
strength of the current and the effect produced in the ap-
paratus, must be experimentally ascertained by direct
comparison with a voltameter.
But if we are going to compare together the indica-
tions of the two instruments produced by various currents,
the second instrument cannot be much more sensitive than
the voltameter, and what advantage can arise from em-
ploying such an instrument 1 This leads us to the fact,
that whereas in a voltameter there is only one way by
which the production of the gas can be more easily mea-
sured, viz., by diminishing the bore of the graduated
tube t (Fig. 5), up which the liquid is forced by the
production of the gas, there are two quite distinct ways
in which the magnitude of the deflection of a ^* galvano-
meter"* needle can be more easily read. The first consists
in using a microscope or some magnifying arrangement,
or in simply lengthening the pointer, both of which
methods correspond with using a tube of smaller bore in
a voltameter ; the second consists in winding a long fine
wire, instead of a shorter thicker wire, on the bobbin of
the galvanometer, and which causes the deflection of the
magnet to be greater with the same current. This
second mode has no analogy with any possible change
in a single voltameter.
Now experiment shows that a galvanometer of a par-
ticular shape and size, and with a definite magnetic needle ^
acted on by a definite controlling force, produced say by
the earth's magnetism, or by som^ fixed permanent magnet,
has a perfectly definite law connecting the magnitude of
the deflection with the strength of the current producing it,
* While a ^^ galvanoscope" is the name given to an instrument used
for ascertaining whether a current is flowing, or merely which of two
currents is the stronger, a "galvanometer" is the name given to an
instrument by means of which the relative strengths of currents can be
compared. Any galvanoscope when calibrated becomes a more or lesa
sensitive galvanometer.
22 PRACTICAL ELECTRICITY. [Chap. I.
altliougli the absolute value of the current in amperes
necessary to produce any particular deflection can be in-
creased or diminished by using fewer turns of thick wire
or more turns of fine wire to make a coil of the same
dimension. If, for example, with a particular gauge of
wire employed to fill up the bobbin it requires 2§ times
as many amperes to produce a deflection of 40° as it re-
quires to produce a deflection of 20°, then if a much
finer gauge of wire be employed to fill the bobbin there
will still be required 2f times as many amperes to pro-
duce a deflection of 40° as are required to produce a de-
flection of 20°. But in the second case yo^qo o^ ^^
ampere may be all that is required to produce the 20°
deflection, whereas five auiperes may be required to pro-
duce the same deflection in the first. The law of the
instrument remains the same, although its sensibility may
be increased 5,000 times by using finer wire to wind
on the bobbin.
Thus, while we take advantage of the absolute charac-
ter of the amount of chemical action to furnish us with
our " standard current meter" we avail ourselves of the
variation that can easily be made in the deflection of a
galvanometer needle corresponding with the same current,
to furnish us with instriunents of greater and greater
degrees of delicacy.
11. Meaning of the Relative and the Absolute
Calibration of a Galvanometer. — Two distinct things
are required to be known with reference to a particular
galvanometer : first, the law connecting the various de-
flections with the relative strength of the currents required
to produce them; secondly, the absolute values of the
currents, that is, the number of amperes required for the
same purpose, or, what is suflficient if the first has been
ascertained, the number of amperes required to produce
some one deflection. The first is sometimes called the
" relative calibration" the second the " absolute calibra-
tion " of the galvanometer.
A galvanometer with its bobbin wound with thick
Chip. I.] RELATIVE AND ABSOLUTE CALIBRATION. 23
Wire may be compared directly with a voltameter,
and the relative calibration of the galvanometer de-
termined ; then if the same space on the bobbin be
wound with any other gauge of wire the relative cali-
bration of the galvanometer will be the same, and there-
fore known, provided that neither the length of the
suspended magnet nor the magnitude of the controlling
force is in any way altered. Or if a galvanometer
wound with thick wire be compared with a voltameter,
and its absolute calibration determined, and if, further,
the law of change of sensibility with gauge of wire has
also been ascertained experimentally, then the absolute
calibration of the same galvanometer, when wound with
any gauge of wire, filling the same space, will be known
without further experiments, provided that the length
of the suspended magnet and the magnitude of the con-
trolling force remain unaltered.
If the length of the suspended magnet, or, more accu-
rately, the distance between its "magnetic poles" remains
unaltered, a change in the strength of its poles will
neither affect the relative nor the absolute calibration
of the galvanometer. For when the current is sent round
the galvanometer, the suspended magnet takes up a
particular position, because in that position the forces on
its two ends, due to the current, balance the control-
ling force produced by the earth's magnetism or by some
permanent magnet. And as any variation of strength
of the poles of the suspended magnet will alter these two
sets of forces exactly in the same ratio, they will still
balance one another for the same position of the sus-
pended magnet.
A magnet whose length is great compared with its
breadth and thickness, acts as if all the magnetism were
concentrated at its two ends, or the magnetic poles are at
its ends. If the breadth or thickness be not small com-
pared with its length, the poles are not quite at its ends,
and the distribution of magnetism along the bar may be
measured as follows.
24
PRACTICAL ELECTRICITY.
[Chap. I.
11a. Measuring the Distribution of Magnetism in
a Permanent Magnet. — This may be done with the
apparatus shown in Fig. 5a, where M m is the permanent
magnet placed on a board, one end of which is attached
Fig. 5a.
to a hinge, while the other end can be raised or lowered
by turning the " micrometer screw " s.* L L is a brass
bar, supported on knife edges at f, like the beam of an
ordinary balance, and on the upper surface of this beam
there v?, a series of equidistant grooves^ in any one of
which can be placed a knife edge made like a hook, and
from which hangs a brass box, w, containing leaden shot.
A soft iron ball, b, hangs by a thread, which passes
* A micrometer screw is a screw of small pitch, accurately cut,
and provided with a large head, the circumference of which is accu-
rately subdivided. If the distance between two of the threads of the
screw be, say ^^^th of an inch, and the circumference be subdivided
into 200 equal parts, the screw will advance TsVxith of an inch when the
head is turned through a space equal to one division.
Chap. I.] DISTRIBUTION OP MAGNETiyM ALONG A BAR. 25
through a small vertical hole in the beam, from a brass
pin p, to which the thread is attached. Before the magnet
is placed on the board, the quantity of shot in this
box and the counterpoise c are so adjusted that when the
knife edge supporting w is placed in the groove marked
nought, the beam rests horizontal. Turning P winds
up, or unwinds, a little of the thread, and^so slightly
raises or lowers the ball. The experiment is performed
by first cleaning the upper surface of the magnet and the
lower surface of the ball with fine emery cloth, and
wiping off" the emery. The board is next levelled, the
magnet put on it, and the pin p turned until the ball is
just in contact with the magnet, when the left-hand end
of the beam is resting at the bottom of the slot s s, in
which position the beam is horizontal. The knife edge
carrying the weight is now placed in the difierent grooves
on the upper edge of the beam until, by trial, two are
found close to one another, such that if the knife edge is
put in the one of them nearer the fulcrum f the iron ball
remains in contact with the magnet, when the micrometer
screw s is turned without shaking, so as to lower the
magnet — or in other words the left-hand end of the beam
rises up as the magnet is lowered, — whereas if the knife
edge carrying w be put in the next groove, the magnet
cannot pull the ball down with it when it is lowered — or
turning the micrometer screw s so as to lower the magnet,
fails to raise the left hand end of the beam. It may
then be assumed that if the knife edges were put about
half-way between these two adjacent grooves, the weight
w would produce a force exactly equal to that exerted by
the magnet on the ball, and which, therefore, is known.
Of course the experiment should be repeated several
times, hanging the knife edge first in one of the
grooves and then in the other, to make quite sure that
the two right grooves have been found, and that the
detaching of the magnet was not produced by shaking.
The magnet is now moved along the board to a new
position, and the force which is exerted when the iron
26 PRACTICAL ELECTRICITY. [Chap. I.
ball is put in contact with another part of it ascertained
in a similar way, care being taken that in all cases the
thread is quite vertical. If experiments be made at
points equidistant from one another all along, say, the
central line of the magnet, it will be found that the
force exerted by the magnet on the ball is very large
towards each end, rapidly diminishes as we approach the
centre, and becomes practically nought at the middle of
the magnet. If similar experiments be conducted along
a line parallel to the long edge of the magnet, but much
nearer to one edge than the other, similar results will be
obtained, but the forces at the ends of the magnet will be
even greater than before. If the magnet be " uniformly
magnetised " the attraction of the iron ball will not indi-
cate any difference between the forces at two points
similarly situated relatively to the two ends of the
magnet, but if we approach our bar magnet m m to a
suspended compass needle we find that the north -seeking
end of the compass needle is attracted by one end of the
bar magnet and repelled by the other, and so for the
south- seeking end of the compass needle.
Hence, although the forces exerted on a piece of soft
iron by points symmetrically situated relatively to the
two ends of a uniformly magnetised steel bar are the
same in every respect, the forces exerted by the two ends
of the large magnet on one end of a compass needle are
opposite in character.
Further, if we slip the bar magnet m m through a
stirrup of paper suspended by a filament of unspun silk,
and place it so that it is balanced and turns freely, we
can find which is its north-seeking and which is its south-
seeking pole, by observing the position it takes up
relatively to the earth. This being done we note that it
was the north-seeking pole of our large magnet that
attracted the south-seeking pole of the compass needle, and
repelled the north-seeking pole. Hence we are led to the
general rule that similar poles repel one another, dis
similar poles attract one another.
Chap. I.]
CALIBRATING A GALVANOMETER.
27
12. Experiment for Calibrating a Galvanometer
Relatively or Absolutely. — Fig. 6 shows a volta-
meter V, connected up with a galvanometer G, and a
" box of resistance coils " R, ready for use for a relative or
for an absolute calibration experiment. The course of
thfe current is shown by the thick and dotted lines ; the
thick lines representing the wires above, and the dotted
lines the wires underneath, the board on which the ap-
paratus is placed, and by means of which it can be moved
Fig. 6.
about from place to place without disconnecting the in-
strument. T T are the terminals, or binding screws,
to which the wires coming from the battery, dynamo
machine, accumulators, or other source of electricity, are
attached. The galvanometer in this case consists of a
vertical circular coil of wire G, at the centre of which is
suspended a very short magnetic needle carrying a long
pointer of aluminium or of brass wire, or, best of all, made
of a thin thread of glass. ^ is a shallow circular box, with
a glass lid. A scale is fixed to the bottom of the box,
and from the centre of the glass lid the small magnetic
needle hangs by a filament of unspun silk. The posi-
tion of the pointer on the scale cau easily he read off if
28
PKACTICAL ELECTRICITY.
[Chap. I.
the ends of the pointer are blackened, and parallax*
can be avoided by fixing the scale close under the
pointer. As this, however, is liable to lead to one or
other of the ends of the pointer touching the scale,
if the instrument is not very well made and carefully
levelled, it is better to avoid parallax by fastening the
scale, which in this case takes the form of a mere circu-
lar ring, to a disc of looking-glass, and by the observer
always taking care, when making a reading, to hold his
head so that the
pointer exactly hides
its reflection in the
looking - glass under-
neath it.
Fig. 7 shows the
interior of the resist-
ance box B, which con-
tains coils of wire w\
&c., wound on wooden
or ebonite bobbins B,
&c. The ends of these
coils are soldered to
stifi" wires Wy which
again are fastened to
the brass pieces c^, C^,
c*, &c., the latter being screwed to the wooden or ebonite
top, E E, of the resistance box. When a plug p- is
inserted tightly between the contact pieces, c^ and c^
(which can be best done by giving to the plug a down-
ward screwing motion) the current flows along the short
path, c2 p2 C'"^, across the metal plug, and practically
none through the wire wound on the bobbin w^. If,
however, a plug p^ be withdrawn, then all the current
passes through the coil w^, and none across the space
Fig. 7.
* Parallax is the error arising from looking at the pointer rather
sideways, instead of looking directly down on it, and so causing its
end to appear to be over a part of the scale a little to the right, or a
little to the left, of its true position.
Chap. L] CALIBRATING A GALVANOMETER. 29
separating c^ and c^. Hence, by taking out one or more
plugs the path for the current may be lengthened at
will,* and the strength of the current diminished. The
brass pieces, c^, c^, c^, are undercut^ as seen in the figure,
so that a strip of clean washleather can be inserted
between them, and the ebonite cleaned. If the ebonite
between the brass pieces were left dirty there would be
leakage of the electricity across the film of dirt when the
plug was removed, and the resistance between two of the
brass pieces would be a little less than that of the coil of
wire connecting them. {See § 140, page 266.)
For the benefit of those who may be accustomed to
use resistance coils, it may be noticed that in the particular
experiment shown in Fig. 6, it is quite unnecessary to
know the length or gauge of the wire that has been
wound on the various bobbins, nor is it at all necessary
that all the coils should be made of the same wire, since
whatever resistance be inserted in the box r, the cur-
rent that passes through the voltameter is the same as
the current that passes 'through the galvanometer, so
that the variation in strength of the current is known
from the voltameter observations, and not from the
length of wire that has been introduced into the circuit.
Indeed the resistance box in this experiment may be
dispensed with altogether when there is any easy mode
of altering the current strength by using different num-
bers of cells or a different kind of battery to produce
the current, but in practice this result is generally most
easily attained by the use of a box of resistance coils.
The calibration is performed by observing for a num-
ber of different currents the rise of the liquid in the gra-
duated tube of the voltameter v (Fig. 6), in a given time,
and the corresponding steady deflection of the needle, or of
the pointer, of the galvanometer. More accurate obser-
vations can be made if, instead of observing the different
lengths of the tube through which the liquid rises in the
* Fvirtber details of the construction of resistance coils will be
found in § 89, pag« 151 ; § 94, page 159 ; § 95, page 1G3.
30 PRACTICAL ELECTRICITY. [Chap. I.
same time corresponding with the different currents, the
times be noted during which the liquid rises through a
fixed length of the tube, say the whole of it, and from
these results a calculation be made of the distances
through which the liquid would have risen in the same
time. In this case two marks only are necessary, one at
each end of the tube.
If the tube t (Fig. 5) has been graduated in cubic
centimetres or cubic inches, and if the apparatus be so
constructed that it can be kept during the experiment
under water, so that the temperature of the gas is the
same as that of the water, and therefore can be easily
measured by a thermometer dipping into the water, then
the actual currents in amperes producing any particular
deflection on the galvanometer will, from what is given
previously on page 12, be known, or the galvanometer will
have been calibrated absolutely. If, however, the tube
has been divided into portions having equal volumes, but
of unknown value in cubic centimetres, or in cubic inches,
or if, what is approximately the same in the case of a
well-drawn tube, the divisions merely mark off equal
lengths of the tube, then the result of the experiment will
merely give the relative calibration of the galvanometer.
13. Graphically Recording the Results of an Ex-
periment.— The results of this experiment, and indeed of
all experiments, are best recorded graphically by points
on a sheet of squared paper,* that is, paper subdivided
into a number of small squares, by a large number of
straight lines drawn at right angles to one another. The
* Prior to the commencement of the courses at the Finsbury
Technical College, in 1879, squared paper was practically used in
England only for the recording of results of original experiments.
And as these results, rather than the training of the experimenter,
were the most important part of the investigation, the paper was
very accurately divided, and sold at a high price totally out of the
reach of students. It became, therefore, necessary to have squared
paper specially made, cheap, and at the same time suflBciently accu-
rately divided for students' purposes ; and such paper, machine-ruled,
can now be obtained at between a farthing and a halfpenny per sheet,
or at about one-twentieth of the cost of the older squared paper.
Chap, i.]
GkAPHlCAL RECOKi) OF RESULTS.
31
distances of the points from o y (Fig. 8) should be taken
to represent the deflections on the galvanometer g, and
the distances of the same points from o x the correspond-
ing amounts of gas produced in a given time, that is, the
corresponding values of the current. In Fig. 8 the two
sets of lines at right angles to one another, which divide
10^ j:w" :b 30" 'W}~
galvanometer deflection
Fig. 8.
the paper^nto squares, have been omitted to avoid con-
fusion. They will, however, be seen on referring to
Fig. 93, page 245.
It may be asked how distances along a line can re-
present the angular deflections on a galvanometer, or
the amount of gas produced in a given time. What is
meant is this : the line o x is subdivided into a number
of equal divisions by the ruling on the squared paper ;
one or any convenient number of these subdivisions is
taken arbitrarily to stand for 1°, then any deflection is
represented by this number of divisions that we have
arbitrarily taken to stand for 1°, multiplied by the num-
ber of degrees on the deflection. Similarly one or any
convenient number of the divisions along o y is taken
arbitrarily to stand for one cubic centimetre of gas, or
the volume, it may be, contained in unit length of the
tube, then any number of cubic centimetres, or the
volume contained in any length of the tube, will be re-
presented by the number of divisions along o y that has
32 PRACTICAL ELECTRICITY. [Chap. I.
been taken to stand for one cubic centimetre, or for unit
length of the tube, multiplied into the number of cubic
centimetres, or into the length of the tube.
In selecting the scale, that is, in determining the
number of divisions along o x or along o y, that is to be
taken to represent 1° deflection, or unit volume of the
tube, we must remember that it is desirable that the curve,
which we are about to draw, shall be as large as possible,
since the larger it is the more accurately we can draw it.
The scale should, therefore, be so selected that the maxi-
mum deflection of the galvanometer that has been used
in the experiment should be represented by nearly the
whole of o X, and the corresponding maximum quantity
of gas developed in the given time by nearly the whole
of o Y, since with this arrangement the curve would occupy
nearly the whole of the sheet of squared paper. For ex-
ample, suppose that the length o x is divided by the ruling
of the paper into 170 equal divisions, and o Y into 100,
and suppose that the maximum galvanometer deflection
was 60°, and that when that deflection was produced the
liquid ascended from the zero mark at the bottom of the
tube to the top mark in twenty-two seconds, then, if
one minute be the fixed time decided on, the most suit-
able scales for distances measured along o X and along
0 Y would be selected as follows : —
60
= 2-8
about.
60
22
= 2-7
))
100
2-7
= 37
)j
2*8 divisions per 1^ would be a little awkward to em-
ploy when deflections of 17°, 29 1°, &c., had to be repre-
sented j 2 J divisions per 1°, or 25 divisions per 10**,
would therefore be better. 37 divisions along OY, to
represent the whole length of the tube would just
Cliap.I.l GBAPHIOAL BECORDS OF RESULTS. 33
enable the maximum volume, corresponding with 2*7
lengths of the tube in the minute, to be represented by
the whole of o y ; but 37 divisions for the whole length
would be a little awkward to employ when other lengths
of the tube had to be represented ; probably, therefore,
30 divisions along o y, to stand for the whole of the tube,
would be more convenient.
Having obtained a sufficient number of points by ex-
periment, a curve should be drawn connecting these points.
Such a curve can be best drawn by bending an elastic
piece of wood, and holding it so as to pass as nearly as pos-
sible through all the points that are plotted on the squared
paper to record the results, and then using the bent piece
of wood as a ruler, along which to draw a line. But unless
the experiment has been performed with great accuracy
— to attain which requires, not merely the careful at-
tention of those engaged in making the experiment, but a
certain amount of practice in experimenting — it must not
be expected that a curve so drawn will pass through all
the points ; some of them, 6, are sure to be a little too
low, meaning that the deflection on the galvanometer has
been read too high, or that the rise of liquid in the
graduated tube has been read too low, from, perhaps,
an error having been made in taking the time, or from
the current not having been kept on for a sufficient time
before the pinch-cock c (Fig. 5) was closed for the gas to
have commenced to come off regularly. Some of the
points e (Fig. 8), on the other hand, are sure to be too
high, meaning that the deflection on the galvanometer
has been read too low, or the rise of liquid in the graduated
tube too high ; or it may be that the experiments were
fairly well made, and that b and e are merely plotted
incorrectly, and so do not represent the results of the ex-
periment.
14. Practical Value of Drawing Curves to Graphic-
ally Record the Results of Experiments. — It may
be asked. But is it not possible that the points b and e,
g^lthough not on the curve, may be quite correct? The
34 PRACTICAL ELECTRICITY. [Chai>. I.
answei is. No. because experience makes us quite sure, from
the fact that the connection between the deflection of the
galvanometer G and the current strength must be a con-
tinuous one, that the points correctly representing the
true connection must all lie on an elastic curve, or on
such a curve as can be obtained by bending a thin piece
of wood or steel, and, consequently, that if, no mistake
has been made in plotting the points h and e, some mis-
take must have been made in taking the observations.
But what is even more important, we are also sure that
the points h' and e on the curve, obtained by drawing
lines through h and e respectively parallel to o y, give
far more accurately the relative strengths of the currents
producing respectively the two deflections in question,
than the currents obtained directly from the experiment
itself. Drawing the curve, then, corrects the results ob-
tained hy the experiment. But it does something more
than that — it gives, hy what is called 'Hnterpolation," the
results that would have been obtained from intermediate
experiments correctly made, that is to say, it tells us what
would be the relative strengths of the currents that
would produce deflections intermediate between the de-
flections that were actually observed. For example,
suppose it be required to know the strength of current
which will produce a deflection of 43°, for which deflection
no experiment has been made, compared with that which
will produce a deflection of, say 27°, for which deflection
also no experiment has been made, then all that is neces-
sary is to draw a line parallel to o y, through the point
A in ox corresponding with 43°, similarly to draw a
line parallel to OY, through the point b in ox, corre-
sponding with 27°, and observe the lengths of the lines
between o x and the points p and Q, where they cut the
curve, then the strength of the current which produces
the deflection 43° on this particular galvanometer bears
to the strength of the current that produces the deflection
27° the ratio of the length a p to the length b q.
If the curve is an absolute and not merely a relative
Chap. LI
GRAPHICAL RECORDS OP RESULTS.
35
calibration curve, then the scale on which it is drawn
will be known, and therefore the number of amperes cor-
responding with either a p or b Q.
The method of plotting the results of experiment on
squared paper, and drawing a curve through them to
graphically record the result, has a third important use in
that it enables us to see the nature of the law connecting the
current with tlie deflection^ which might easily escape
observation if only a few disconnected experiments had
been made. For example, suppose that the results ob-
tained in some particular case are : —
flection.
Relative Strength of Current.
10
24.
17-3 .
41-5.
22-8 .
64-7.
29-5 .
70-8.
37-4 .
89-7.
then plotting the results on squared paper a straight line
is obtained, and from this we see at once that this par-
ticular galvanometer has, somehow or other, been so
made that the angular deflection of the needle is directly
proportional to the strength of the current.
36
CHAPTER II
GALVANOMETERS.
15. Tangent Galvanometer— 16. Scale for a Tangent Galvanometer—
17. Mode of Making a Tangent Scale— 18. Best Deflection to use
with a Tangent Galvanometer — 19. When the Tangent Law is
True— 20. Preceding Conditions are fulfilled in the Tangent Gal-
vanometer— 21. Adjusting the Coil of a Tangent Galvanometer —
22. Variation of the Sensibility of a Galvanometer with the
number of Windings and with the Diameter of the Bobbin —
23. Thomson's Galvanometer for Large Currents — 24. Values
in Amperes of the Deflections of a Tangent Galvanometer con-
trolled only by the Earth's Magnetism— 25. Galvanometers having
an Invariable Absolute Calibration — 26. Calibrating any Gal-
vanometer by Direct Comparison with a Tangent Galvanometer —
27. Pivot and Fibre Suspensions — 28. Sine Law : under what
Conditions it is True — 29. Preceding Conditions are fulfilled
in the Sine Galvanometer — 30. Calibrating a Galvanometer by
the Sine Method — 31. Calibration by the Sine Method of the
Higher Parts of the Scale— 32. Calibration by the Sine Method
with a Constant Current —33. Method of Making a Sine Scale —
34. Portable Galvanometer with Approximately Invariable Abso-
lute Calibration — 35. Construction of Galvanometers in which the
Ajigular Deflection is Proportional to the Current — 36. Shielding
Galvanometers from Extraneous Magnetic Disturbance — 37. Direct
Beading Galvanometers— 38. Advantages of the Previo\is Types
of Galvanometers — 39. Ammeter,
15. Tangent Galvanometer. — Using the particular
galvanometer of the shape shown as g (Fig. 6), experi-
ment proves that the calibration curve has the shape
shown in Fig. 9, page 37, if —
(1st) The controlling force be produced by the needle
moving in a " uniform magTietic field," like that produced
by the earth's magnetism, and in which the force acting
on a given magnetic pole is uniform in magnitude and
direction ;
(2nd) The diameter of the bobbin round which the
wire is wound be large compared with the length of the
suspended magnetic needle ;
Chap. II.3
TANGENT GALVANOMETER.
37
(3rd) The centre of this needle be at the centre of
the bobbin ;
(4th) The plane of the bobbin be so placed that it
contains the " magnetic axis " of the needle, that is, the
Fitr. 9.
line joining its magnetic poles, when no current is passing
round the coil.
And it is easy to ascertain by measurement that
if any three points, p, Q, R, be taken on this curve,
the lengths A p, b q, c r, parallel to 0 y, bear to
one another the ratios of the tangents* of the angles
* To find the tangent of any angle A o b (Fig. 10). In either line
o A or o B take any point P, and drop a perpendicular P Q on the other.
Then in the triangle p o Q we have two perpendiculars •. one; P Q,
38
PRACTICAL ELECTRICITY.
[Chap. XL
represented oy o A, o b, and o c respectively. Such a gal-
vanometer is, therefore, called a " tangent galvanometer"
Fig. 11.
and it may be henceforth used without reference to any
voltameter for the comparison of current strengths,
as they will be simply proportional to the tangents
opposite to the given angle ; the other,
o Q, adjacent to it ; and a third side,
opposite the right angle, called the
hypotenuse. The ratio of the opposite
side to the adjacent side is called the
tangent of the angle A o B,
or LS = tan. A O B.
OQ
The ratio of the opposite side to the
hypotenuse is called the sine of that
angle.
Fig. 10.
OP
sm. A 0 B.
Chap. II.] MAKING A TANGENT SCALE, 39
of the angles through which the magnetic needle is
deflected.
16. Scale for a Tangent Galvanometer.— The scales
of tangent galvanometers are frequently simply divided
into degrees, and a reference has constantly to be made
to a table of tangents to enable the galvanometer to be
used. A better plan is to divide the scale, not into equal
divisions, but into divisions, the lengths of which become
smaller and smaller as we depart from the zero or un-
rig. 12.
deflected position of the needle, in such a way that the
number of divisions in any arc is proportional, but not
necessarily equal, to the tangent of the angle corre-
sponding with that arc. Or the scale may, as shown in
Fig. 11, be divided into degrees on one side, and on
the tangent principle on the other.
17. Mode of Making a Tangent Scale. — Fig. 12
shows the method of constructing such a tangent scale.
The lengths A b, b c, CD, &c., along the line A f, which is a
tangent to the circle at the point A, are all made equal
to one another ; hence if from the centre, o, of the circle
straight lines, o a, o b, o c, &c., be drawn, cutting the cir-
cumference of the circle in the points a, 1, 2, 3, &c., the
40 PRACTICAL ELECTRICITY. [Chap. II.
numbers 1, 2, 3, 4, &c., will be respectively proportional
to the tangents of the angles a o 1, a o 2, A o 3, &G,
For tan. A o 1 = —
o A
AC
tan. A 0 2 = —
DA
_ 2 AB
OA
tan. A o 3 = —
O A
_ 3 AR
A ~ OA
and so on.
Beginners are apt to think that, because the divisions
on such a tangent scale are very much crowded together
in the higher part of the scale, the value of a current can
be more accurately ascertained by taking a reading on
the degree side, and then finding the value of the tangent
in a table of tangents, than by reading it ofi" on the tangent
scale. But this seeming greater accuracy is quite delusive,
since what has to be ascertained in either case is the
tangent of the angle, not merely the angle, and although
on the degree side of the scale the angle can be read much
more accurately than can be its tangent, or a number pro-
portional to its tangent, on the other side, this only indi-
cates that the error of a tenth of a degree in a large angle,
although a much smaller proportional error than a tenth
of a degree in a smaller angle, produces a far greater pro-
portional eiTor in the tangent. For example, if 20° '1
be read instead of 20°, the error is g^o? whereas if 85°-l
be read instead of 85°, the error is only g^, or less
than a quarter of the preceding error. But the tangents
are in the first case 0-3659, and 0*3640, the error in the
tangent, therefore, is aifo, or about y^, whereas the
tangents in the second case are 11-66 and 11-43, so that
Chap, n.] WHEN THE TANGENT LAW IS TRUE. 41
the proportional error is yfls^, or about -^j which is
nearly four times as great as before. Hence in this case,
when the proportional angular error is diminished to one-
quart 3r, the corresponding proportional error in the tan-
gents is increased four times. The crowding together of
the divisions on the tangent scale at the higher readings
is, therefore, a correct indication of the inaccuracy likely
to occur in taking readings in that part of the scale.
18. Best Deflection to use with a Tangent Gal-
vanometer.— It can be shown that if one current strength
has to be measured by a tangent galvanometer, the result,
other things being the same, will be most accurate when
the deflection produced is 45° ; or if two currents are to
be measured, the measurements will be most accurate
when the deflections are as nearly as possible at equal
distances on the two sides of 45°.
19. When the Tangent Law is True. — Any galvano-
meter may now be calibrated either relatively or abso-
lutely, by comparison with a tangent galvanometer ; and
if the galvanometer to be calibrated be a very sensitive
one, a tangent galvanometer with a bobbin wound with
fine wire should be selected. Before, however, entering
into the calibration of other galvanometers in this way, it
may be well to consider under what circumstances a gal-
vanometer will be a tangent galvanometer, especially as
beginners are too apt to think that if the law of some
galvanometer is unknown to them, then it must be the
tangent law.
The apparatus shown in Fig. 13 enables us to decide
under what conditions a force acting on a body turning on
a pivot is proportional to the tangent of the angle through
which the body is deflected from the position it had before
the force acted on it. A short piece of wood, n n', turning
on a pivot, o, is acted on by a weight, w, which produces a
force constant both in magnitude and direction. Variable
weights, w', are put into the scale-pan hanging at the end
of a long cord, which passes over a distant pulley, /?, and
which is attached at its other end to the piece of wood
42
PRACTICAL ELECTRICITY.
[Chap. II.
at N. The height of the pulley, j), is such that the long
portion of the cord is horizo7ital when n n' is vertical,
that is, when there is no weight in the scale-pan, which
in the figure is shown holding a weight, w'. And owing
to the pulley being distant from n n', the long portion of
the cord remains nearly horizontal, even when the piece
Fig. 13.
of wood N n' is deflected through an angle. Under these
circumstances experiment shows that the weights w' put
successively into the scale-pan are proportional to the
distance s P, intercepted between the position s on the
scale where the cord supporting w cuts the scale when
N n' is vertical, and the point P where the pointer p n cuts
the scale when n n' is deflected by the weight put into the
scale-pan. Now this length s p divided by s o is the
tangent of the angle through which N n' is deflected, and,
Chap. II.] WHEN THE TANGENT LAW IS TRUE. 43
therefore, since s o is a constant length, » p is proportional
to the tangent of the angle through which N n' is deflected.
Hence with the apparatus the tangent law holds. What
are the conditions of the apparatus 1 They are : —
1st. The controlling force is unaltered in magnitude
and direction by the motion of N n'.
2nd. The deflecting force always acts in the same
direction, and at right angles to the controlling force.
Hence, whenever these two conditions are fulfilled
the deflecting force will be nieasured by the tangent of
the angle of deflection.
20. Preceding Conditions are Fulfilled in the Tan-
gent Galvanometer. — The first condition, constancy in
magnitude and direction of the controlling force, is prac-
tically fulfilled in all galvanometers where the controlling
force is produced by a distant magnet, since such a mag-
net produces a practically uniform magnetic field through-
out the space in which the galvanometer needle can
move, for, as the length of the needle is small compared
with its distance from the poles of the controlling magnet,
the controlling force exerted on the needle cannot be
materially altered in magnitude and direction when it is
deflected. In all galvanometers, therefore, in which the
controlling force is due to the attraction produced by the
earth's magnetism, condition (1) is absolutely fulfilled.
Next with reference to condition (2) — with all flat coils
the magnetic force due to a current passing round them
is perpendicular to the plane of the coil for all points in
the plane of the coil. But the direction of this force
rapidly alters as we proceed outside the coil, unless we
are near the axis, in which case the direction of the force
remains practically perpendicular to the plane of the coil.
And, indeed, for all points on the axis itself the magnetic
force is strictly perpendicular to the plane of the coil, that
is, acts along the axis. In Fig. 14 are seen a number
of lines, called " lines of force." These lines tell us the
paths along which a magnetic pole would be pulled, or
pushed, by the action of a current passing round a circular
44
PRACTICAL ELECTRICITY.
[Chap. II.
wire or coil* perpendicular to the paper, and cutting it in
the two small circles c c. It will be seen that at any point
p on the axis a a of the coil the direction is everywhere
perpendicular to the plane of the coil, also that near the
axis the direction is nearly perpendicular to this plane for
Fig. 14.
a considerable distance, while near the coil itself the
direction of the force changes rapidly- Hence, if we sus-
pend at the centre of a coil a very short magnetic needle,
m m, having a length not greater than one-tenth or one-
* This wire or coil, the plane of which is in reality perpendicular
to that of the paper, is represented in the figure in a kind of oblique
perspective by a double line.
Chap. 11.] COIL OP A TANGENT GALVANOMETER. 45
twelfth the diameter of the coil, the deflecting force due
to a current passing round the coil will be perpendi-
cular to the plane of the coil, even after the needle is
deflected, and will be also perpendicular to the controlling
force, if the controlling force acts in the plane of the
coil, that is, if the coil is so placed that its plane contains
the magnetic axis of the suspended needle when no cur-
rent is passing through the coil.
In fact, if the coil occupies the position of the semi-
circular wire seen in Fig. 13, and if this wire is in the
^^ plane of the magnetic meridian,^'* the conditions neces-
sary for the deflecting force being proportional to the
tangent of the deflection will be fulfilled.
We have seen, from the experiment described in § 15,
page 36, that the tangent of the deflection of the needle
of a tangent galvanometer is directly proportional to the
current strength, or simply to the current ; hence, we
may conclude that the force acting on a magnetic pole at
a fixed point on, or near, the axis of a circular coil is
directly proportional to the current flowing round that
coil. Later on we shall see that this law is true for a
fixed magnetic pole in any position relatively to the coil
acted on by a current flowing round a coil of any shape.
It is not necessary that the coil of a tangent galva-
nometer should be circular, but in order to obtain the
straightness of the lines of force in the neighbourhood of
the axis, as seen in Fig. 14, and not merely for points
actually on the axis, of which we could only avail our-
selves by using an infinitely short magnet, the diameter
of all parts of the coil must be large. Hence, if an
elliptic, or other non-circular coil, were used, its smallest
diameter would have to be large, and consequently its
largest diameter unnecessarily so.
From what has been said, and from an examination
of Fig. 1 4, it will be seen that for very small deflections
of the needle any galvanometer, no matter what be the
* The "plane of the magnetic meridian" at any place is that
vertical plane in which lies the sais of a compass needle.
46 PRACTICAL ELECTRICITY. FCliap. H.
size of the needle and of the coil, or how near be the con-
trolling magnet, will be a tangent galvanometer. And
further, since the tangents of very small angles are simply
proportional to the angles, the deflections of the needle,
as long as they are very small^ in any galvanometer are
directly proportional to the strengths of the currents pro-
ducing them.
21. Adjusting the Coil of a Tangent Galvanometer.
— Returning now to ordinary tangent galvanometers to
be used for large deflections, how can we adjust the coil
so as to be sure that its plane contains the axis of the
needle? Owing to the coil having a certain breadth, it
is impossible to see the needle when looking down on to
the coil ; indeed, it is for this reason that the long light
pointer attached to the needle is placed at right angles
to the needle. It would not be right to assume that be-
cause the instrument has been so turned that the pointer
points to the zero on the scale, therefore the plane of the
coil contains the magnetic axis of the needle, for even if
the scale has been attached to the instrument so that the
line of zeros is at right angles to the plane of the coil, it
does not follow that the pointer itself is at right angles
to the needle. The two may even have been placed at
right angles to one another by the maker, and yet the
pointer may have been bent subsequently, so that they
are not at right angles at present ; or no experiment may
have been made by the maker to test this, as he is aware
that the user will probably make a test and adjust the
pointer for himself. This test may most simply be made
as follows : — Turn the instrument until the pointer points
to 0°, send any convenient current through it, and observe
the deflection, then reverse the direction of the current
without altering its strength, and observe the deflection on
the other side. If these deflections are exactly equal, then
the plane of the coil contains the axis of the needle when
the pointer points to 0°, and the instrument is properly
adjusted. But if, on the other hand, one deflection is,
say, 47° to the left, and the other, say, 44° to the right, the
Chap. II. J ADJUSTING A TANGENT GALVANOMETER COIL. 47
pointer is not at right angles to the magnetic axis of the
needle, supposing, of course, that the scale has been so
fixed that the line of zeros is exactly at right angles to
the plane of the coil. Next, turn the instrument a little
about its centre in the direction opposite to that in
which the needle moved when the greater deflection was
obtained. The pointer will now, of course, not point to
zero ; let it stand at 1° to the left. Again send a current,
first in one direction, obtaining a deflection, say, 46° to
the left, and in another direction, when it gives a deflec-
tion of, say, 45° to the right. Now remembering that the
pointer started from 1° to the left, the true deflections of
the needle are respectively, 46° - 1°, or 45° to the left,
and 45° +1°, or 46° to the right. Hence, the fault is
now on the other side, or the left deflection is smaller than
the right, and we have, consequently, turned the instru-
ment too much. Turn, therefore, the coil round a very
little in the opposite direction, so that when no current
is passing through the instrument the pointer stands at,
say, ^° to the left, and send as before reverse currents
of equal strength, obtaining apparent deflections, 45 J° to
the left and 44J° to the right, which, corrected for the
initial zero error, correspond with equal deflections of
45° to either side.
The instrument will now be correct when it is so
placed that for no current the pointer stands at J° left,
and it can be so used, but not, however, with the tan-
gent scale. To enable us to employ the side of the
dial graduated in tangents, as well as to avoid having to
remember the J° left error, do not alter the position of
the instrument, but bend the pointer until it points to
0° for the same position of the instrument in which
it previously pointed to J° left. The instrument will
now behave as a correct tangent galvanometer when the
pointer stands at 0° for no current.
We have spoken of reversing the direction of the cur-
rent without altering its value. This may be done by
causing the current to pass through any galvanoscope,
48 PRACTICAL ELECTRICITY. [Chap. H.
the law of which may be quite unknown ; and taking care
that the deflection of the needle after the current has
been reversed is the same in amount as it was before
the current was reversed ; indeed, if we reverse the
connections of the galvanoscope at the same time that
we reverse the connections of the battery or other cur-
rent generator employed in the experiment, it will not be
even necessary to know that the coil and needle of this
auxiliary galvanoscope are symmetrical, or that the
strength of a current producing a deflection to the
right is the same as that of a current producing a de-
flection to the left.
22. Variation of the Sensibility of a Galvanometer,
with the number of Windings and with the Dia-
meter of the Bobbin. — A tangent galvanometer, on the
bobbin of which a short thick wire has been coiled, can be
calibrated absolutely by direct comparison with a volta-
meter. To obtain a more delicate tangent galvanometer,
we must replace this thick wire with many turns of fine
wire, and the numbers of amperes or fractions of an
ampere producing any particular deflection on this deli-
cate galvanometer will also be known if we know the
exact change in the sensibility produced by replacing the
thick wire with many turns of fine. The apparatus shown
in Fig. 15 is for the purpose of enabling this to be ex-
perimentally tested, as well as for testing the variation in
sensibility produced by altering the diameter of the coil.
g g is a. flat cylindrical box, containing, as in Fig. 6, a
scale fastened to its bottom, and a short needle carrying
a long light pointer, suspended by a short piece of unspun
silk, fastened to the centre of a circular piece of glass,
forming the cover, c C is a bobbin of large diameter, and
such that its centre is exactly the same height above the
base-board b b as is the centre of the suspended magnetic
needle, c c is a smaller bobbin, of which the diameter is
exactly half that of the larger bobbin, but still large com-
pared with the length of the suspended magnet. The
centre of the smaller bobbin is also on the same level
Chap. II.] SENSIBILITY OP A GALVANOMETER. 49
as the suspended magnet when the base-board 6 5 of the
smaller bobbin is placed on that of the larger. On the
larger bobbin c c are wound two distinct coils of insulated
wire, one consisting of twelve convolutions, and having its
ends attached to two of the binding screws, 1, 2, the other
Fig. 15.
of four convolutions, and having its ends attached to the
other two binding screws, 3, 4. If the binding screw 2 at
the end of the first coil be joined by a piece of wire, as
shown in the figure, to the binding screw 3 attached to
the beginning of the second, the current will go 12 + 4,
or sixteen times round the bobbin ; whereas if the wire
connect the end of the first coil, 2, with the end of the
60 PRACTICAL ELECTRICITY. tChap. IL
second. 4. and the current enter and finally leave the
bobbin by the two binding screws 1, 3, attached respec-
tively to the beginnings of the two coils, then the current
will go twelve times round the bobbin in one direction
and four times in the other, or practically 12-4, or
eight times round the bobbin. Now, experiment shows
that if the controlling magnet be untouched, and a cur-
rent of constant strength be passed successively first four,
then eight, then twelve, then sixteen times round the
bobbin, which is kept fixed in position during the expe-
riment, the tangents of the corresponding deflections pro-
duced will be as four to eight, to twelve to sixteen, that is,
simply proportional to the number of times the current
passes round the bobbin. The constancy of the current
can be tested by the deflection on the auxiliary galvano-
scope G, and if the insertion in the circuit of the greater
or less number of coils on the bobbin c c, or any other
cause, tends to make it vary in strength, its constancy
can be maintained by sliding the screw clip s along the
stretched wires w w,* by means of which the length of the
wire in the circuit can be increased or diminished, and
the current strength diminished or increased. If we next
experiment with the bobbin c c of half the diameter, and
on which a coil of four convolutions is wound, we find
that if the two bobbins be placed so as to be in one plane,
and if their centres coincide with that of the suspended
magnet, the tangent of the deflection produced by a
certain current flowing round the smaller one is twice as
great as the tangent of the deflection produced by the
same current flowing four times round the larger bobbin ;
and also if the same current pass four times round the
smaller in one direction, and eight times round the larger
in the opposite direction, that no deflection is produced.
* To prevent these wires being accidentally damaged, it is better
to put them in a groove formed in the base-board instead of above the
board as shown in Fig. 15. In that case it is convenient to shape the
clip 8 so that it can sHde in the groove in the base -board, the ends of
the clip being guided by the sides of the groove.
Chap. II.l SENSIBILITY OF A GALVANOMETER. 61
From this we learn that the tangent of the deflection
produced by a current, that is, the sensibility of the
instrument is directly proportional to the number of
convolutions of wire^ and inversely proportional to their
diameter. On the bobbin c c the sixteen convolutions of
wire all occupy practically the same position relatively to
the suspended magnet. If, however, many turns are to
be wound on a bobbin, the bobbin will have a certain
depth in the direction of the diameter of the coil, and a
certain width at right angles to the plane of the coil. The
error introduced by the depth of the coil is that of making
the convolutions of wire have different diameters, and
the effect of this we have just seen. The error intro-
duced by the width of the coil can be seen by observing
how the' deflection produced by a constant current varies
as the bobbin cc is moved parallel to itself along
its axis. The additional error introduced by the non-
centring of the coil and the needle may also be experi-
mentally investigated by examining how the deflection
produced by a constant current alters as the bobbin is slid
in its own plane.
It is not necessary in this book to consider exactly
how to correct these errors, nor the error arising from
the diameter of the bobbin in all actual tangent galva-
nometers not being infinitely large compared with the
length of the needle ; and it will be sufficient to state
that with a tangent galvanometer made with a single
bobbin having a rectangular channel, within which the
coils of insulated wire are to be wound. Prof. Silvanus
Thompson has shown that the tangent law is most ac-
curately fulfilled when the depth of the channel in the
radial direction bears to the breadth in the axial direction
the ratio of
'v/3to\/2,
or about eleven to nine.
When an experiment is made to determine the altera-
tion in sensibility produced by moving the coil parallel to
52 PRACTICAL ELECTRICITY. [Chap. II.
itself along its axis, it is found that the tangent of the de-
flection produced by the same current when a coil of radius
r is made to occupy different positions parallel to itself at
distances x, measured along the axis from the centre of
the needle, is proportional to
that is, the sensibility of the galvanometer is proportional
to this expression.
Example 9. — A tangent galvanometer is made with
two coils of equal diameter, the first consisting of 500
convolutions of wire, the second of one convolution. If
a current of 0*25 ampere sent through the first cause a
deflection of 45°, what current sent through the second
in the opposite direction, while the same current was
still flowing through the first, would cause the deflection
to become one of 10° ]
Let X be the unknown number of amperes :
^ 500x0-25 -a; tan. 10°
Then
500 X 0-25 tan. 45°
Answer. — 103 amperes.
Example 10. — A galvanometer is about to be con-
structed of two coils : the first, six inches in diameter,
consists of 350 convolutions of wire ; the second has
two convolutions only. A current of 0*4 ampere sent
through the first causes a deflection of 30°. What must
be the diameter of the second coil, in order that a cur-
rent of 80 amperes, in the opposite direction, sent through
it, while 0*4 amperes is still flowing through the first,
may cause the deflection to become 5° %
Let X be the diameter of the second coil.
Since the effect of the current is directly proportional
to the number of convolutions, and in\*ersely proportional
to the diameter —
Chap. II.T Thomson's LARGE CURRENT GALVANOMETER. 53
0-4 X 350 80 X 2
6 " X tan. 5°
0-4 X 350 tan. 30°
6
Answer. — 8 inches nearly.
Example 11. —A galvanometer is about to be con-
structed of two i;oils : the first, seven inches in diameter,
consists of 600 convolutions of wire ; the second is to
be 5*5 inches in diameter. A current of 0*1656 ampere
sent through the first causes a deflection of 40°. Oi
how many convolutions of wire must the second coil
consist, in order that while 0*1656 ampere is still flowing
through the first, a cun-ent of 65 amperes fiowing through
the second may cause the deflection to become 8° 1
Answer. — One convolution.
23. Thomson's Galvanometer for Large Currents.—
A tangent galvanometer, with a scale graduated in tan-
gents, and controlled by a permanent magnet rigidly fixed
to the instrument, has been arranged by Sir William
Thomson, and is shown in Fig. 16. It has the peculiarity
that the needle, scale, and permanent magnet m can be
slid along a board p, and so withdrawn parallel to itself
farther and farther from the action of the coil c ; hence a
wide range of sensibility can be given to the instrument, in
accordance with the last formulas. To prevent the current
which flows in the long wires connecting the galvano-
meter with the rest of the circuit acting directly on the
suspended magnetic needle, these coming and going wires
are twisted together into a form of cable, which is shown
in the figure, and which is supplied with the instrument.
The advantage of this galvanometer is that, first, owing
to its being a tangent galvanometer the ratio of two
current strengths can be very accurately compared;
secondly, from the method of sliding the needle away from
the coil, two currents, widely differing in strength, can be
compared. The disadvantage is that, on account of the
H
PRACTICAL ELECTRICITY.
[Chap. II.
small action that the coil, even with a very strong cur-
rent flowing round it, can exert on the needle, when
they are at opposite
ends of the
board, the controlling
force of the perma-
nent magnet has to
be kept small ; hence
the instrument, as we
shall see afterwards,
cannot be made very
''dead beat "(see ^38,
page 78), and fur-
ther, the indications
are much disturbed
by any external mag-
net. In fact,the in-
strument is rather for
use in a laboratory,
where the magnetic
field is constant in
strength, and known,
than in a dynamo
room or workshop,
where large pieces of
iron and powerful
magnets are being
moved about.
24. Values in
Amperes of the De-
flections of a Tan-
gent Galvanometer
controlled only by
the Earth's Mag-
netism.— The sensi-
bility of a tangent
galvanometer depends not merely on the bobbin, but also
on the strength of the controlling field. If, however, the
Chap, n.] TANGENT GALVANOMETER WITH EARTH CONTROL. 55
^^ horizontal component of the earth* s magnetic force^** in
London be alone employed as the controlling force, and
if the instrument be used with the centre of the coil and
the centre of the needle coinciding, then the connection
between the current A in amperes, the deflection d in
degrees, the radius r of the coil in inches, and the number
of convolutions N of wire on the bobbin, is given by
the following equation for 1886 :
^ _ 073735 X r X tan, d,
N
the coeflicient 0*73735 for 1886 becoming 073844 for
1887, 0-73953 for 1888, and 0-74062 for 1889. From
this it follows that in the year 1887 a deflection of
45° will be given by one ampere when there are five
convolutions of wire on a bobbin 6-772 inches in
radius.
Example 12. — How many amperes would deflect the
needle of a tangent galvanometer 60° in the year 1886,
the controlling force being the horizontal component of
the earth's magnetism, and the galvanometer having
a bobbin five inches in radius, wound with six con-
volutions of wire %
mr, 1 r • 0-73735 X 5 X <v/3
The number of amperes is — - .
Answer. — 1-064 amperes.
Example 13. — Through what angle would 0-598
ampere deflect the needle of a galvanometer with a
bobbin seven inches in radius, wound with five con-
volutions of wire, in the year 1888, the controlling
force being the horizontal component of the earth's
magnetism 1
* The horizontal component of the earth's magnetic force is that
portion of the earth's force which acts on a compass needle.
bo PRACTICAL ELECTRICITY. [Chap. U.
0-598 = 0-73953 x 7 x tan. rf
, • . tan. d =
6
5 X 0-598
0-73953 X 7
= 0-5775
d= 30°. Answer.— ZO''.
Having tan. c?, d may be found either by looking in a
table of tangents or in the following way : —
Take a sheet of squared paper, and on it select two
axes, or lines of reference, ox, o y, at right angles to one
another. Choose any number of the divisions on your
paper to represent unity, taking care that there are more
than 100 of these larger divisions along ox, and at least
58 along oy. These numbers are chosen because the
tangent of the angle required is approximately given by
57-7
the ratio YT^p* Along ox mark off o a, equal to 100 of
the divisions, then on the line through a, parallel to
o Y, mark off a b as nearly as possible equal to 57*7 of the
divisions. Join o b. Then b o a is the angle d,
Fortan. boa = ^
o a
57-7
100
= tan. d.
The angle d may now be found by means of a pro-
tractor.
Example 14. — If the horizontal component of the
earth's magnetism in 1887 be the controlling force in a
tangent galvanometer, the bobbin of which is 11 inches
in diameter, how many convolutions of wire must be
wound on the bobbin in order that a current of 1'015
amperes may give a deflection of 45° I
Answer. — 4 convolutions.
Chap. II.] INVARIABLE ABSOLUTE CALIBRATION. 57
Example 15. — If the horizontal component of the
earth's magnetism in 1885 be the controlling force in a
tangent galvanometer, the bobbin of which is wound
with eight convolutions of wire, what must be the radius
of the bobbin in order that a current of 0"384 ampere
may give a deflection of 50°"? Answer. — 3 J inches.
Tan. 50° may be found either in a table of tangents
or in the following way : —
Take a sheet of squared paper ; on it take axes o x,
o Y ; with a protractor make the angle box, equal to
50°, and produce o b as far as the paper will allow. Let
A b be the farthest line from o, parallel to o y, which cuts
b o. Then tan. 50° = — .
o A
Count the number of divisions and fractions ol a
division in a b and o A, and divide the one by the othei.
If the angle be large, great care must be taken to lay
it down accurately with the protractor, since a small
error in a large angle will introduce a large error in the
tangent.
Example 16. — About how many times the horizontal
component of the earth's magnetism must the controlling
force be in a tangent galvanometer, having a bobbin five
inches in radius wound with six convolutions of wire, in
order that a current of 20 amperes may make a deflection
of 45° 1 Answer. — Nearly 32J times.
25. Galvanometers having an Invariable Absolute
Calibration. — In order that the absolute calibration of
any galvanometer may remain invariable, the magnetic
field in which the suspended magnet moves must remain
constant in strength ; and if the galvanometer is to be
moved about near masses of iron, or near the large power-
ful electromagnets of dynamo machines, probably the
most satisfactory of all the methods that have been tried
for securing approximate constancy of the controlling
field is either to attach a powerful permanent magnet
to the instrument, or still better to substitute the force of
58 , PRACTICAL ELECTRICITY. [Uhap. II.
a spring for a magnetic controlling force.* In either
case this controlling force must, of course, be large
compared with any magnetic forces that are likely
to be exerted by outside magnets on the suspended
needle, and must be very many times as large as that
due to the earth's magnetism. But, in that case, un-
less the instrument is only to be employed to measure
the most powerful currents, the coil must be near the
needle, so that the condition (No. 1, page 36) for obtain-
ing the tangent law cannot be complied with. And gene-
rally the necessity of having a coil of very large diameter
compared with the length of the needle makes a tangent
galvanometer unsuitable for a portable galvanometer, or
else necessitates the employment of so short a needle that
its oscillations are much impeded by the mass of even an
extremely light pointer attached to it. Hence with all
portable galvanometers, and especially in the case of those
which may be used near masses of iron or dynamos
without serious error, it is better to abandon any attempt
to obtain the tangent law, and calibrate the galvano-
meter by direct comparison with a tangent galvanometer.
26. Calibrating any Galvanometer by Direct Com-
parison with a Tangent Galvanometer. — Fig. 17 shows
the simplest way of doing this. G is the standard
tangent galvanometer, d the galvanometer, which, if
rough and portable, is sometimes called a "detector,"
requiring to be calibrated, v is a vessel containing two
zinc plates dipping into a small quantity of a solu-
tion of zinc sulphate, which is used for varying the
strength of the currents passing through g and d by
altering the distance between the bottoms of the plates.
The wires coming from the generator of electricity
are attached to the terminals, one only of which, t,
is seen in the figure, and a key placed between g and
D enables the current to be made or broken. As the
same current passes through g and d, it is quite unneces-
* For further information on shielding galvanometers from extra-
neous magnetic disturbance, see § 36, p. 73 ; 1 53, p. 103 ; and § 202, p. 390.
Chap. II.] CALIBRATING, USING TANGENT GALVANOMETER. 59
sary to know the value of the resistance introduced by v ;
all that has to be done is to observe a number of cor-
responding deflections of the needles of g and of d, then,
since the true value of the current is proportional to the
tangent of the deflection in g, a calibration curve can be
drawn for D, in which horizontal distances represent the
observed angular deflection of the needle of d, and verti-
cal distances the relative strengths of the currents pro-
ducing these deflections. If the number of amperes
Fig. 17.
producing any particular deflection in g is also known,
then D will be calibrated absolutely.
It frequently happens that, on account of the great
increase in sensitiveness produced by putting the wires
conveying the current close to the needle, a rough galva-
nometer with a few turns of wire is even more sensitive
than a tangent galvanometer with many turns. Under
such circumstances it would be difficult to compare them,
as a large deflection on d would only correspond with a
small one on G, and a smaller deflection on d would not
produce deflections on g large enough to be read at all
accurately. This difficulty may, however, be overcome by
putting a piece of wire s (Fig. 17), a '■^ shunt " as it is called,
60 PRACTICAL ELECTRICITV. [Chap. II.
between the terminals of d, and which allows a portion
of the current to pas^s through it instead of through
D. As, however, for the same shunt the same fraction
of the total current is, as we shall see later on (page 178),
always shunted past d, the sensibility alone of D, and
not the law connecting current strength with de-
flection, is altered by using such a shunt. The use of
a shunt, therefore, alters the absolute but not the rela-
tive calibration of a galvanometer ; consequently, if D is
absolutely calibrated, the same shunt must always be
employed when it is desired to use the absolute calibra-
tion curve of that galvanometer.
27. Pivot and Fibre Suspensions. — The galvano-
meters G and D differ also in another particular, namely, in
the way in which the magnetic needle is supported. In d
the little magnet has a jewel in its centre, and rests on a
sharp pivot, as in an ordinary pocket compass ; whereas
in G the needle is supported by a fine fibre of unspun
silk, the upper end of which is rolled round a brass pin
hj by turning which the needle can be lowered on to the
card s s, on which the scale is engraved, when the instru-
ment is being carried about, or raised again so as to be
in the centre of the coil when the instrument is in use.
The fibre suspension introduces far less friction to the
motion of the needle than the best jewel and pivot, and,
in addition, costs far less ; but with a fibre suspension it
is generally necessary that the instrument should have
levelling screws, such as are seen attached to G, Fig. 17,
and that it should be levelled before being used.
There is one form of fibre suspension, however, which
is used by Sir Wm. Thomson in his " marine galvano-
meter^^ and which, although not employed in other in-
struments, has advantages that make it worthy of more
general adoption in portable galvanometers. To a silk
fibre stretched between a fixed support and one end of a
spring, there is attached the magnetic needle and pointer,
or other indicating arrangement, and when these are well
balanced, the whole instrument may be tilted through
Chap. II.]
WHEN THE SINE LAW IS TRUE.
61
several degrees without any practical alteration of the
deflection. {See § 53, page 103.)
28. Sine Law : Under what Conditions it is True.
— When the controlling force acting on the needle of a
galvanometer remains constant in magnitude and direc-
tion on the needle being
deflected (a result that
will always practically
happen when the control-
ling force is produced by
the attraction of a distant
magnet), there is a very
simple plan, suggested to
the author by Prof. Carey
Foster, for calibrating the
galvanometer relatively
by employing what is
known as the " sine prhv-
ciple,^^ in a particular way,
and which does not require
the use of any other gal-
vanometer at all. We
have already seen under
what conditions a force
acting on a body is pro-
portional to the tangent of
the angle through which
the body is deflected, and
in a similar way the ap-
paratus shown in Fig. 18
will enable us to decide under what circumstances a force
acting on a body is directly proportional to the " sine "
of the angle of deflection, n o is a piece of wood, in this
case not necessarily short, turning on a pivot at o, and
having suspended from its lower end a weight w, which
produces a force constant both in magnitude and direc-
tion. The same end of the piece of wood n o is also
acted upon by a force produced by a cord carrying the
Fig. 18.
62
PRACTICAL ELECTRICITY.
[Chap. XL
scale-pan in which is placed the weight w', the magnitude
of which can be varied. Now experiment shows that, if
different weights be successively put into the scale-pan,
and if in each case the framework a b carrying the
pulley c be turned about the centre o, so that the piece
of wood N 0 always occupies the same
position relatively to A b, the weights
are proportional to the horizontal dis-
tance (s s. Fig. 19), measured along
the scale between the point where the
cord carrying w cuts now, and where
it cut it when w was nought. But s s,
or PN, which ig equal to it, divided
by N o, the half-length of the deflected
lever, is equal to the sine of the angle
PON, through which n o has been de-
flected. It is also obvious that turning
A B, so that it always takes up the
same position relatively to n o, is only
a means of causing the angle between
the cord carrying w' and no to be
constant, in order that the only change
in the force exerted by the string
carrying w' may be that caused by the
change of weight, not by any change
in the direction of the pull. From
this we conclude that in order that a
force acting on a body turning on an
axis may be directly proportional to
the sine of the angle through which the
body is deflected :
1. The controlling force must he
constant in magnitude and direction.
2. The deflecting force, although variable in its direc-
tion in space, must he fixed in direction relatively to the
deflected hody.
29. Preceding Conditions are Fulfilled in the Sine
Galvanometer. — In any galvanometer in which the con-
Cbap. II.J SINE GALVANOMETER. 63
trolling force is produced by the earth's magnetism, or by
any distant fixed magnet, this force will be constant in
magnitude and direction, and independent of the needle
changing its position ; also the deflecting force produced by
the current passing round the bobbin, can be made to have
an invariable direction relatively to the needle, if the
bobbin, or the framework of the instrument to which the
bobbin is attached, be turned round after the deflected
needle ; for it will be found that, although on turning the
bobbin the needle turns away from the bobbin, it does
not turn as fast as the bobbin. Under these circum-
stances, the sine of the angle through which the needle
has been deflected from the position of rest which it had
when no current was passing through the bobbin, will be
directly proportional to the current strength. Now, if
the coil be placed so as to have a fixed position relatively
to the needle, both when no current passes thruugh the
coil and when a given current passes through the coil,
then the angle through which the coil has to be turned from
the first position to the second, is the same as the angle
through which the needle has been deflected ; and hence,
in the so-called sine galvanometers, there is, in addition
to the scale moving with the bobbin, an independent
fixed scale, to show through what angle the coil has been
turned. This, however, is not absolutely necessary, since,
if, after the coil has been turned until it has the fixed
position relatively to the needle, the current be inter-
rupted, without the position of the instrument being
disturbed, then the needle will swing back, and, after a
few oscillations, will take up its original undeflected posi-
tion, the angle between which and its deflected position
will be the angle of which the sine has to be taken.
As a current passing through a coil has usually the
greatest effect on a magnetic needle suspended inside it
when the axis of the needle is perpendicular to the axis of
the coil, this is the fixed position of the coil relatively to the
needle usually adopted, and the one in which the pointer
stands at 0° on the movable scale. But this particular
64 PRACTICAL ELECTRICITY. fChap. H.
position is not at all necessary for the fulfilment of the.
sine law, and therefore special precautions need not be
adopted, as in the case of the tangent galvanometer (see
ante, page 45), to insure the axes of the needle and of
the coil being at right angles when the pointer stands at
zero on the scale.
Any galvanometer which is controlled by a distant
magnet, and which can be turned round a point that is
approximately the centre of the needle, can hQ used as a
sine galvanometer, and, therefore, can be calibrated by
the employment of the sine principle. All that is neces-
sary to be done to make a measurement is as follows : —
Place the instrument so that the pointer points to some
fixed mark on the scale ; 0° is a convenient mark, but not
a necessary one; then send any convenient current
through the galvanometer, obtaining a deflection of, say,
d°. Turn the instrument until the pointer again points
to the fixed mark on the scale. Stop the current, and
observe through what angle lt° the needle comes back.
Di° will, of course, be larger than d°. Now turn the in-
strument round, so that the pointer points to its original
mark on the scale, 0° for example, and repeat with a
second current, obtaining in the same way deflections
d°, T>2°. Then the currents producing the deflections
d° and c?2° respectively with the galvanometer, are pro-
portional to the sines of d^^ and T>°.
30. Calibrating a Galvanometer by the Sine Method.
— Fig. 20 shows an apparatus arranged for calibrating
the galvanometer in this way. Three little blocks of wood,
two only of which, c c, can be seen in the figure, are
temporarily fixed so as to allow the galvanometer to be
turned round without shifting its position, a precaution
of practically no consequence if the controlling force be
due to the earth's magnetism alone, but desirable if the
whole or part of the controlling force is produced by a
not very distant magnet. Of course the magnet must be
so far away that neither the magnitude nor direction of
its attraction on the suspended needle is altered by the
Chap. II.] CALIBRATING BY THE SINE METHOD.
65
turning of the needle ; but this need not be very far, unless
the needle employed is long, v is a vessel containing two
zinc plates for adjusting the strength of the current in
the manner described in a previous experiment, w is
one of the wires leading to the current generator, and
T is the terminal to which the other is attached.
To calibrate a galvanometer by the employment of
the sine principle, requires the current in each case to
remain constant long enough for the instrument to be
Fig. 20.
turned round after the needle, until the two are in a
fixed position relatively to one another. But when once
the calibration curve has been drawn, a galvanometer so
calibrated can, of course, be used to measure currents as
transient as a galvanometer calibrated in any other
way.
31. Calibration by the Sine Method of the Higher
Parts of the Scale. — If the first deflection is more than about 45°
it is found impossible to use the sine principle in the ordinary way,
because, on attempting to turn the coil after the deflected needle,
so as to bring the fixed mark on the scale under the pointer, the
needle moves so far round in advance of the coil that at last the
66
PRACTICAL ELECTRICITY,
[Chap. TI.
attraction of the earth or other controlling magnet begins to
assist the current instead of opposing it. The equilibrium then
becomes unstable, and the needle swings right round. The cali-
bration of the higher parts of the scale, however, may be effected by
the sine method, by using currents which produce a first deflection of
less than 45'*, in the following way : — Select some other starting-
point, say 40^ on the scale, for the zero, that is, let the galvano-
meter be turned, so that the pointer points to -f 40", when no
current is flowing ; now send a current through the galvanometer,
deflecting the pointer to, say, -j- 60** (Fig. 21). Next, turn the
galvanometer round
until the 0" division,
or whatever fixed
mark was previously
used in §§ 29 and
30, comes under the
pointer. Lastly, stop
the current and let
the pointer now take
up a position — 30''
say; then, when the
galvanometer is
Fig. 21. placed in the ordi-
nary position, so that
the pointer points, say, to 0**, when no current is passing, the
current that will deflect the pointer to 60** will be
8in^30°j< sin. 60*^
sin. (60^—40'') '
or, generally, the current that will deflect the pointer to any angle
d° will be
sin. D^ X sin. d°
sin. (<?°— 40«) '
where d° is the angle through which the pointer comes back on
stopping the current.
After experiments have been made in the way described
in §§ 29 and 30, and a curve drawn with the values of d° as ab-
scissae, and of D'' as ordinates for values of d'^ up to about 45^,
experiments may be made in the way just described, and the curve
extended by using for the ordinates the values of
sin. D'' X sin. d''
"sm. (c?°— 40^)^ *
The reasoning of this extended method of calibration is as
follows :— From Fig. 19 we see that when ^ needle is controlled by
Chap. II.] CALIBRA TING BY THE SINE METHOD. 67
a uniform magnetic field, the moment of the controlling force* is pro-
portional to p N, that is, to the sine of the angle through which the
needle is deflected. If, then, a galvanometer is so placed that the
pointer points to 0° when no current is passing, it follows that, in
order that a current shall produce a deflection of flJ**, it must pro-
duce a force whose moment is proportional to sin. d°. When,
however, the instrument is turned, as shown in Fig. 21, the cur-
rent which is deflecting the needle to d° produces a force whose
moment is proportional to sin. {d° — 40°). Now, what is the rela-
tive strength of this current measured by the method described in
§§29 and 30? It is proportional to the sin. d®. Hence, a current
proportional to sin. d'' deflects the needle to d° when the con-
trolling force has a moment proportional to sin. {d° — 40°). Con-
sequently, a current proportional to
sin. D° X sin. d°
sin. (<;<>— 40«)
wiU deflect the pointer to rf° when the controlling force has a
moment proportional to sin. d°^ that is, when the pointer points to
0° when no current is passing.
32. Calibration by the Sine Method with a Con-
stant Current. — The following, due to Mr. Mather, is perhaps
the neatest of the methods of calibrating a galvanometer on the
sine principle, since, by means of it, the calibration can be
effected throughout the whole range of the scale, and no other
apparatus than the galvanometer to be calibrated, and a current
generator, such as a " DanielVs cell^^ which will give fairly con-
stant currents, is required. Send a current through the galvano-
meter, such as will produce a deflection of about 30° when the
galvanometer is so placed that the pointer points to 0° when no
current is passing. Next, without varying the current, turn the
galvanometer until the pointer points to about 35°. Stop the
current and observe the position taken up by the pointer when it
comes to rest. Turn the galvanometer round farther and farther,
and repeat, observing in each case the position of the pointer
when the current is flowing, and the position the pointer takes up
when the current has been broken. Also make a series of obser-
vations with the galvanometer placed in such positions that the
first deflection is less than 30°. In some one position of the
galvanometer let d° be the angular deflection from 0° when the
current is flowing, and z° when the current has been interrupted ;
then it follows, from what was stated in § 31, that this current,
which we may call our unit current, passing round the galvano-
* The ^^ moment of a force about a point" is the product of the
magnitude of the force into the length of the perpendicular let fall
from the point on the hne representing the direction of the force.
68
PRACTICAL ELECTRICITY.
[Chap. II.
meter coils, is able to produce a deflecting force whose moment is
proportional to sin. {d° — z^) when the needle is deflected to d°.
Hence it follows that the current which would be necessary to
produce a force whose moment should be proportional to sin. d°
sin cl ^
for the same position of the needle must be -; '—^ — times our
unit current, that is, must be proportional to
am.d°
sin. {d^—z"".)
sin. {d^.—z")
but such a current would deflect the pointer to d° when the galva-
nometer was so placed that the pointer pointed to 0^. for no current
passing. Hence, to obtain the calibration curve, we have simply to
plot values of d° for the abscissae, and the corresponding values of
sm. d°
sin. {d''—z°)
for the ordinates.
33. Method of Making a Sine Scale.— Instead of find-
ing in a table of sines the sines of the various angles through
Fig. 22.
which the needle swings back, we may construct a sine scale in
the following way : — On a p, Fig. 22, any tangent of the circle
Chap. II.] MAKING A SINE SCALE. 69
on which the scale is to be made, mark off equal parts a b, u c,
c D, &c. From b, c, d, &c., draw perpendiculars to a p, b I, c 2,
D 3, &c., meeting the circle in 1, 2, 3, &c.
Then the sines of the angles a o 1, a o 2, a o 3, &c., are propor-
tional to the numbers 1, 2, 3, &c. For drop perpendiculars 1 «, 2 J,
3 c, &o., on oa: r^hen sin. aoi ^ Lf
o 1
O A
since b a equals la, and o a equals o 1.
Similarly sin. a o 2 =
OA
and so on.
Therefore, the sines of the angles are proportional to a b, a c,
A D, &c.
Therefore, they are proportional to the numbers, 1, 2, 3, &c.
If we wish to divide the whole quadrant into an exact number
of subdivisions in this way, we must commence by marking off
on the tangent A p a length at, equal to the radius of the circle,
and then subdivide A f into any desired number of equal parts in-
stead of taking ab, b c, &c., any equal lengths.
If, when using this scale, it be found on sending two currents
thi'ough the galvanometer that the needle deflects through the
angles a o 2, a o 3 respectively, the mistake must not be made of
considering that the currents are in the proportion of two to three,
for this will only be the case when ao2, ao3 are the angles
through which the needle swings back after the galvanometer has
been turned in each case.
34. Portable Galvanometer with Approximately
Invariable Absolute Calibration. — A type of portable
galvanometer (Fig. 23), to which was attached a very
powerful ^^ permanent magnet," having its needle made
of a number of small pieces of soft iron, was made and
calibrated absolutely by M. Deprez, in 1880. The scale
was divided simply into degrees, and a table of numbers
giving the value in amperes of the various deflec-
tions was attached to the instrument. This instrument
rendered considerable service in the early days of
commercial electric lighting, but there were two dis-
advantages in connection with its use : first, as the scale
was divided simply into degrees, the deflection with-
70
PRACTICAL ELECTRICITY.
[Chap. II.
out the use of the table of vahies gave no indication of
the strength of the current measured ; and, secondly, it
was necessary to refer to this table twice over when
measuring two different currents, as the deflection was
not directly proportional to the current. The current,
in fact, increased more rapidly than the angular deflec-
tion, a result which is generally found to occur in ordi-
nary galvanometers, and which arises from the deflection
Chap. II.] PROPORTIONAL GALVANOMETERS. 71
of the needle causing it to move into a position in which
the current passing round the coil acts with less force
on the needle than when it is in the zero position or
parallel to the plane of the coil.
35. Construction of Gralvanometers in which the
Angular Deflection is Proportional to the Current.
— We have already seen (page 43) that the current is
proportional to the tangent of the deflection of the
galvanometer needle, when neither the magnitude noi
direction of the controlling force is altered as the needle
moves into a new position on being deflected, and when,
in addition, the direction of the controlling force is at
right angles to the direction of the force with which the
current passing round the coil acts on the needle.
In order, therefore, that the angular deflection may be
directly proportional to the cun^ent, we must either
cause the needle on being deflected to move into a posi-
tion in which the current passing round the coil acts
more powerfully on it, or into a position in which the
controlling force becomes weaker; or we may arrange
that both these results may be produced.
The first condition may be obtained in a rough way
by employing the very defect of construction previously
referred to in the adjustment of the tangent galvano-
meter, and which made the deflection on one side of the
zero larger than that produced by the same current on
the other — viz., not putting the coil so that its plane was
parallel to the suspended magnet when no current was
passing through the coil. The needle, when deflected to
that side on which the greater deflection is obtained, will,
instead of moving from a stronger to a weaker part of
the magnetic field produced by the current, move at first
into a stronger part, and then afterwards into a slightly
weaker part. The eflfect of this arrangement is to make
the proportional law connecting current and deflection
true for a much larger deflection from the undeflected
position of the needle than if we commenced with the
needle parallel to the plane of the coil for no currents
72
PRACTICAL ELECTRICITY.
[Chap. II.
But this arrangement lias the disadvantage that it can
only be used for currents deflecting the needle to one
side of the scale, for, if the current be flowing in the
opposite direction, the defect of want of proportionality
between current strength and deflection will be in-
creased.
This plan, by means of which the proportionality on
one side of the scale is sacrificed to increase that on the
other, has been employed by the author, and later on by
Pig. 2t.
MM. Carpentier and Deprez, for making proportional
galvanometers.
If the " controlling field " be a uniform field, such as
is produced by the earth's magnetism, that is, if the con-
trolling force acting on the pole of a given magnet is the
same both in magnitude and direction at all points, then
the arrangement shown in Fig. 24, and which has been
worked out by Messrs. Walmsley and Mather, two of
the assistants at the Finsbury Technical College, may be
employed. The instrument consists of two coils shaped
as shown, and the special device consists in fixing them
so that they are separated by a distance a little less than
the length of the needle. The instrument is placed so
that when no current is passing through the coils the
Chap, II.1 SHIELDING GALVANOMETERS. 73
needle hangs symmetrically between them, and it is
found that direct proportionality of current and deflec-
tion up to 45° to 50° is obtained from the fact that, with
the arrangement indicated, the needle, on being de-
flected, moves into a position in which the current acts
more powerfully on it, or shortly into a more powerful
part of the ^^ deflecting field." Galvanometers of this
type are shown in use in Figs. 15 and 20.
36. Shielding Galvanometers from Extraneous
Magnetic Disturbance. — If, however, the instrument is
to be portable, and if it be desired that the deflections of
the needle should be unaffected by the moving about of
neighbouring magnets or pieces of iron, the galvanometer
must be " shielded" and this, as stated in § 25, can be done
by attaching a powerful permanent magnet to the instru-
ment, the action of which on the suspended magnet is far
stronger than that likely to be caused by any other neigh-
bouring magnet. When using such a permanent magnet,
there are two well-defined ways employed by the author
for obtaining direct proportionality. The first consists in
winding the insulated wire on the two halves of a brass
bobbin A (Fig. 25), separated by a brass tube T, in which
the pivoted soft iron needle cariying the pointer moves,
and attaching soft iron pole-pieces p p, hollowed out as
shown in the figure, to the permanent magnet m m. The
wire is wound on the bobbin (which in the figure is
shown unwound), much as cotton is wound on a reel ; nona
is wound on the tube t, and the coils on the two halves
of A are electrically connected with a wire passing by the
side of T ; into the ends of the brass bobbin, soft iron
cores F F are screwed, the outer ends of which are seen
in the figure. The other ends of these soft iron cores
project a considerable distance into the brass tube,
and the result is that on the needle being deflected
from the position it occupies when no current is pass-
ing round the coils, and which is along a diameter
of the tube t at right angles to the axis of A a, its
ends come nearer the noses of these soft iron cores
74
PRACTICAL ELECTRICITY.
[Chap. II.
inside the bobbin a a. Hence the deflecting force
grows much stronger as the soft iron needle is deflected.
The alteration in the strength of the controlling force
depends on the exact curvature given to the ends of the
soft iron pole-pieces p p, which embrace the brass tube T.
Fig 25.
If the curvature of the pole-pieces is
that of the tube t, and the pointed
pieces be pressed against the tube so
needle as nearly as possible, then the
trolling field will somewhat increase
the needle is deflected, since the ends
come nearer the iron of the pole-pi<
much greater than
edges of the pole-
as to approach the
action of the co7i-
in strength when
of the needle will
when the needle
Chap, n.] SHIELDING GALVANOMETERS. 75
is deflected ; whereas, if the curvature of the ends of the
pole-pieces be much less than that of the tube — if, in fact,
the ends of the pole-pieces be nearly flat — then the action
of the controlling field will become weaker as the needle
is deflected.
When no soft iron cores fp are employed, the
" straight line '' or ^^proportional" law can be produced by
taking advantage of the fact that the deflecting field
increases in strength as the needle is deflected, in conse-
quence of its poles entering more into the coils wound
on the two halves of the bobbin A A. In that case the
ends of the pole-pieces p p should only be very slightly
curved. For the purpose, however, of making the
final adjustment for sensibility, to be described a little
farther on, the use of the soft iron cores f f screwed,
more or less, into the ends of the bobbin is found to be
very convenient, and, as already explained, their pre-
sence leads to the deflecting force much increasing in
strength as the needle is deflected. The result of this
is that the correction is too great, that is to say, instead
of the angular deflection increasing less rapidly than the
current, which is the ordinary result obtained with gal-
vanometers, the deflection would increase much more
rapidly than the current, giving a flat instead of a steep
calibration curve. To avoid this over-correction the cur-
vature of the pole-pieces must be considerable.
The final result then obtained is as follows : — If the
cores F F are too far in, the calibration curve is flat, that
is, the angular deflection increases more rapidly than the
current ; if too far out, the calibration curve is steep, or
the angular deflection increases less rapidly than the
current ; but between these two limits there are several
positions of the cores giving nearly perfect proportionality
between deflection and current. Within these limits the
cores may be adjusted, and the sensibility of the instru-
ment altered. If they be screwed out, it will require a
larger current to produce the same deflection ; while, on
the other hand, if they be screwed in, the opposite effect
76
PRACTICAL ELECTRICITY.
[Chap. IL
will be produced. Hence, within these limits, any deflec-
tion may be made to correspond permanently with any
current.
37. Direct-Beading Galvanometers. —Hence, by the
Fig. 26.
employment of these cores, we can not only construct
an instrument in which the deflection shall be directly
proportional to the current, but we can use a dial
graduated in amperes instead of in degrees, and so ob-
tain a " direct - reading galvanometer " as shown in
Chap. II.]
DIRECT READING GALVANOMETER.
77
Fig. 26.* For, although it would be very difficult to fill
the bobbin with a particular gauge of wire, so that with
a particular controlling magnet a given number of
amperes shall produce exactly a particular deflection, it
is easy by trial to approximate to this, and then finally
adjust the instrument by screwing the soft iron cores a
little in or out until any particular deflection on
the dial is produced by exactly the number of amperes
of currents marked opposite that deflection on the dial.
* See § 221, page 431, for further details regarding the double scale
and commutator p shown in Fig. 26.
78 PRACTICAL ELECTRICITY. [Chap. IL
And should the permanent magnet lose its strength from
time to time, when the instrument will of course become
more sensitive, we can, by screwing out the cores, re-
adjust it so that it will still continue to be a correct
direct-reading galvanometer.
Another plan, and probably a still better one tor
obtaining all the above results, is to make the opening
in the bobbin A through which the pivoted needle is
inserted, in the construction of the instrument, much
smaller, as shown in Fig. 27, so that the wire can be
coiled almost continuously from one end of the bobbin to
the other without the gap in the bobbin necessitated by
the tube t (Fig. 25). With the arrangement of Fig. 27
the deflective force is but slightly increased as the needle
is deflected ; hence, to obtain the proportional line the
controlling force must be made to diminish as the needle
turns, which result can be obtained by curving the ends
of the soft iron poh^pieces in the way shown in p p (Fig.
27) that is, by making them convex instead of concave
to the coil, as was done with the previous arrangement.
38. Advantages of the Previous Types of Galvano-
meters.— All these instruments have the advantages that
their indications are ^'■shielded" that is, are not seriously
affected by the presence of neighbouring magnets or
pieces of iron; secondly, if the needle is well balanced
the instrument can be used in any position without any
error being introduced in the readings ; and, thirdly, as
the needle is very light (or, more strictly, has only a very
small " moment of inertia ")* and as it is moving in a very
powerful magnetic field, the oscillations of the needle are
very quick, and die out very rapidly, so that if the
current that is being measured has a sudden change in
its strength, the needle moves sharply from one point of
the scale to another point, where it stops dead in
* The moment of inertia of a body about any axis is found by
imagining the body divided up into a large number of very small parts,
and taking the sum of the products of the mass of each part into the
BqHiare of i*s distance from the axis.
Cliap. II.] AMMETERS. 79
response to the change in the current strength, or the
instrument is ^^ dead-heat ^^ ; whereas, if a needle of large
moment of inertia were employed moving in a weak
magnetic field, then on any change taking place in the
current strength the needle would simply begin to
oscillate over the scale, and many changes might take
place in the current strength, the current even remaining
constant at each of its vatious values for a very decided
time before the needle would come to rest and allow any
measurements to be taken. The advantage of employing
a dead-heat instrument is very marked when the current
produced by a dynamo worked by a gas-engine has
to be measured. If the instrument is dead-heat every
change in the current produced by the slight change
of speed of the gas-engine at each explosion of the gas is
accurately recorded ; indeed, the slight change of speed
that occurs each time the joint in the driving belt, if it
be a ^\lap-jointy^* and not a ^' hutt-joint," passes over the
driving pulley, is observed ; whereas, if the instrument be
not dead -heat these fluctuations in the current merely
cause the needle to keep up a constant vibration over the
scale, and so prevent any accurate readings being taken.
Other forms of current galvanometers are given
farther on (page 377), and another method of shielding
by putting the galvanometer in an iron box, with very
thick sides, is considered in § 53, page 103, and by giving
the needle a motion of translation in § 202, page 390.
39. Ammeter. — Such a dead-heat direct -reading gal-
vanometer is frequently called an " ammeter j'^ hence the
name on the dial of Fig. 26, and we may temporarily
regard such an ammeter as our commercial instrument
for measuring current strengths in amperes.
0th er, and more modern, types of ammeters are described
farther on (page 382), where also are stated the advantages
and disadvantages of some of the most important kinds.
* A lap-joint is made by putting one end of the leather belt over
the other, and lacing, or riveting, them together; while in a butt-
joint the ends are simply brought together, but not put one over the
other.
80
CHAPTER III.
DIFFERENCE OF POTENTIALS, ELECTRIC QUANTITY, DENSITY,
AND THEIR MEASUREMENT.
40. Difference of Potentials — 41. Potential of the Earth Arbitrarily
taken as Nought — 42. The Difference of Potentials between Two
Conductors does not Measure the Difference in their Electric
Charges — 43. Volt — 44. Measuring Potential Difference by
Weighing — 45. Increasing the SensibiHty of the "Weight Electro-
meter by Using an Auxiliary High Potential — 46. Rough Electro-
meter— 47. Action of a Gold-leaf Electroscope — 48. Objections to
the Ordinary Methods of Constructing Gold-leaf Electroscopes —
49. Conduction and Induction — 50. Potential Uniform at all
Points inside a Closed Conductor — 51. No Force inside a Closed
Conductor due to Exterior Electrification — 52. A Metallic Box
not a Magnetic Screen imless made of Very Thick Iron — 53.
Marine Galvanometer — 54. Reflecting Galvanometers — 55. Angular
Motion of the Reflected Ray is Twice the Angular Motion of the
Mirror — 56. Connection between the Motion of the Image on a
Plane Scale and the Angular Deflection of the Mirror — 57. Static
Electrical Apparatus should be Enclosed in a Metallic Case —
58. Quantity of Electricity — 59. Comparison of Quantities of
Electricity — 60. Quantity of Electricity produced by Rubbing
Two Bodies Together — 61. Object of Rubbing Two Bodies
Together to Produce Electrification — 62. Proof -plane — 63. Electric
Density— 64. Density is Nought on the Inner Surface of a Closed
Conductor — 65. Potential of a Conductor Depends Partly on the
Amount of Electricity on it — 66. Potential of a Conductor
Depends Partly on its Shape — 67. Potential of a Conductor De-
pends Partly on its Position — 68. Modes of Var^ng the Potential
of a Conductor — 69. Examples showing the Difference between
Potential; Density and Quantity — 70. Static and Current
Methods of Measuring Potential Differences Compared — 71. When
a Potential Difference Galvanometer may be Employed — 72. Volt-
meter.
40. Difference of Potentials. — When a current of
electricity is flowing through a wire it has the same
strength at all cross-sections of the wire ; if, for example,
the wire be cut anywhere, and a galvanometer be put in
the circuit, the galvanometer will always show the same
deflection while the same current is flowing. In the
same way in the case of a water-pipe, the quantity of
Chap, ni.] DIFFERENCE OF POTENTIALS. 81
water passing every cross-section of the pipe per second
is exactly the same as soon as the flow of water
becomes a ^^ steady''' one. Just at the commencement,
when, for example, some water has entered at one end
of the pipe, and none has flowed out at the other — when
the pipe is filling, in fact — the flow at different cross-
sections may be different ; so also, in many cases, just
at the moment after completing an electric circuit, the
current will differ at different cross-sections. But as soon
as the flow in each case becomes a steady one this dif-
ference disappears, and the strength of the water current,
that is, the number of gallons of water passing per
minute (not, of course, the velocity of the particles of
water) is the same at all parts of the pipe, even if the
pipe be broad at some points and narrow at others, so
also the strength of the electric current flowing through
a single circuit is " ^*?^^/brm " "^ at all parts of the circuit,
independently of the thickness of the conductor and of
the material of which it is made.
But, although the stream of water is the same at all "
part» of the pipe, the pressure per square inch of the
water is by no means the same, even if the pipe be quite
horizontal and of uniform gauge. This pressure per
square inch of the water on the pipe, which is the same
as the pressure per square inch of one portion of the
water on another portion at the same part of the pipe,
becomes less and less as we proceed in the direction of
the flow, along a horizontal pipe of uniform sectional area.
It is, in fact, this difference of pressure, or " lossof headj"
as it is sometimes called, that causes the flow to take place
against the friction of the pipe, the difference of pressure
at any two points in the case of a steady flow through a
horizontal pipe of uniform sectional area being equal to
* Uniform refers to space, constant to time. The height of
the houses in a street is generally not uniform, but it is constant
as long as there is no change made in the height of the houses.
If water be run out of a cistern the level at all parts of the surface
of the water is uniform, but it is not constant, since it steadily falls as
the water runs out.
82
PRACTICAL ELECTRICITY.
[Chap. III.
the frictional resistance of that length of pipe for that
particular flow.
Quite analogous with this there is, in the case of
an electric current flowing through a conductor, a
" difference of potentials " at two points in the conductor,
and this difference of pote7itials is necessary to overcome
the '^resistance" of the conductor, or opposition that it
ofiers to the passage of an electric current through it.
'^e -^5 ^4 Sg Sa S,
Fig. 28.
The pressure per square inch of the water at any
point in a tube conveying a stream can be ascertained by
attaching a vertical stand-pipe to the tube, and seeing to
what height the water is forced up in this stand-pipe, and
if at a number of points A, B, c, D, E, F (Fig. 28) in a
glass tube 1 1, conveying a stream of water, a series of
vertical glass stand-pipes Sj, Sg, &c., be fixed, the height
to which the water is forced up in them will show the
distribution of pressure along the pipe. If the tube 1 1
be horizontal, straight, and of uniform cross- section, and
if the flow of water be a steady one, then the tops of the
water in the stand-pipes will be found to all lie in one
straight line, from which it follows that the diflference
Chap. III.] DIFFERENCE OF POTENTIALS. 83
of pressure between any two points is proportional to
the distance between the points.
If the screw pinch-cock s be fully, or nearly fully, open,
and that at s' fully open, the stream of water through
the tube tt will be rapid, and the tops of the columns of
water in the stand-pipes will lie in a straight line such as
Ti Ti Tp If the cock s be screwed up a little so as to
squeeze the bit of indiarubber tube (that at s' still re-
maining fully open) the flow will be diminished, and the
line joining the tops of the columns of water in the stand-
pipes will make a less angle with the horizontal, or
occupy a position TgTgTg. As the cock s is screwed
up more and more the line is tilted up more and more,
until at last, when the cock is shut and the water turned
off altogether, the line becomes horizontal, t,jT;,t,„ and is at
the same level as the top of the water in the cistern.
The inclination of this line to the horizontal, therefore,
diminishes as the flow of water diminishes, and becomes
nought when the flow ceases altogether.
So, in the same way, the ^^ electric potential'^ at different
points of a wire conveying a current can be measured
statically by an apparatus that will be described farther on
(§ 75, page 1 30), and if a number of measurements be made
of the potential at different points of a circuit conveying a
current, it will be fovind that the results are smaller and
smaller as we proceed in one direction ; and, farther, if
the conductor be all of uniform gauge, and made of the
same material, and the electric current be a steady one,
it will be found that the difference of potential between
any two points is proportional to the length of the
conductor between these points.
This analogy between the distribution of water-
pressure and of electric potential, is a very useful one for
students in enabling them to grasp the idea of electric
potential ; but, like many other analogies, it must not be
pressed too far; for example, a bend in a pipe, even
with a steady flow of water, is found to cause a falling off
in the water-pressure ; whereas, a bend in a wire has no
84 PRACTICAL ELECTRICITY. [Chap. III.
effect on the electric potential if a steady current is
flowing ; or, again, if there be a sudden expansion or
contraction in a pipe, there is a sudden alteration of
the water-pressure, which has no analogy in any sudden
alteration of the electric potential at a point in a circuit
where the sectional area of the conductor changes
abruptly.
In fact, the flow of water or of gas in a pipe can be
diminished to any extent by a contraction of one point
only, which may be practically effected by partially closing
a tap. For example, if the screw pinch-cock s' be par-
tially closed, a great resistance to the flow of the water
will be introduced at this point, shown by the fact that
the line joining the tops of the columns of water in the
stand-pipes now breaks up into two portions Tg Tg Tg and
Tg' Tg' Tg', parallel to one another, but the one much below
the other ; whereas, if an electric circuit consist of many
yards of wire, no appreciable alteration of the current will
be produced by making only half an inch of the wire
have, say, one-tenth of its previous sectional area. If,
however, the current be so strong as to fuse the wire, then
the current will become nought, just as the stream of
water or gas becomes nought on the tap being entirely
closed, and the analogy of fluid and electric flow will
again hold.
41. Potential of the Earth Arbitrarily taken as
Nought. — Unfortunately the statical measurement of
electric potential is not nearly as simple as the statical
measurement of fluid pressure, in consequence of
the forces produced by the mutual attractions of any
two ordinary bodies charged with electricity being very
small. Potential has also to be measured relatively, in
the way that temperature is usually measured, and not
from a zero, or starting-point, as can be employed in the
measurement of length or weight. The same length may
be called one yard, or three feet, or thirty-six inches, or
91-44 centimetres, but a length that is nought on any one
of these systems of measurement is nought on them all ;
Chap, m.] earth's POTENTIAL TAKEN AS ZERO. 85
whereas, not only is the temperature which is called 15°
on the Centigrade scale called 59° on the Fahrenheit, but
the temperature that is called 0° on the former is called
32° on the latter. In the measurement of temperature,
then, we take the temperature of some definite body and
call it 0°, and we do not imply by doing so that no lower
temperature can be obtained ; so, in the measurement of
potential we take the potential of a certain body and
call that potential nought — the electric potential that is
arbitrarily taken as nought being that of the earth.
In thus taking the potential of the earth as the
potential level to measure from, no assumption is made as
to the eai-fch having no charge of electricity on it ; indeed,
so far from that, experiment shows that the earth
produces exactly the same electrical effects as it would if
it were " negatively " or " resinously " electrified : that is,
electrified in the same way as is a piece of ebonite after
being rubbed with a piece of dry flannel, and oppositely
electrified to a piece of dry smooth glass, which, after
being rubbed with a piece of dry silk, is said to be
" positively ^^^ or " vitreously,^^ electrified.
Measuring potentials relatively to that of the earth
is simply like measuring heights above the Trinity water-
mark, or measuring longitude east or west of Greenwich.
42. The Difference of Potentials between Two Con-
ductors does not Measure the Difference in their Electric
Charges. — The fact that two conductors differ in poten-
tial tells us nothing about the quantities of electricity in
either of them, nor whether these quantities are positive or
negative, nor even whether either of the bodies is charged
with electricity at all {see 8, § 69, page 124). All that we
can deduce from the fact that two conductors, made of the
same material, differ in potential is that if they be joined
by a wire there will be a flow of electricity, or a current
from one to the other, until this difference of potential is
destroyed ; and we say that the one from which ^^ positive "
electricity flows has the " higher potential" or a " positive
'potential" relatively to the other. In the same way, by
86 PRACTICAL ELECTRICITY. ICliap. IIL
knowing the fact that the pressure of the gas in two
gas-holders is different, we have no information as to the
quantities of gas in either of the vessels, but we merely
are sure that, if the vessels be joined by a pipe, gas will
flow from the vessel in wliich the pressure is greater into
that in which it is less as long as any difference in
pressure remains. So, in the same way, if two vessels
standing on the table contain water, and if we merely
know that the level of the water in one of them is higher
than that in the other, we can tell nothing about the
number of gallons of water in the two vessels ; but what
we do know is, that quite irrespectively of the size of the
vessels, or of the quantity of water in them, if the two
vessels be joined together by a pipe anywhere below the
lower water-level, water will flow from that in which the
level is higher into that in which it is lower until this
difference of level is destroyed.
So, again, we can form no conception from the fact
that one body is hotter than another as to the amount of
heat either will give out in cooling down to the freezing
temperature, or even which of the two will give off the
greater amount of heat when so cooled ; the existence of
a difference of temperature between two bodies only
justifies us in concluding that if the bodies be so placed
that heat can pass from one to the other, heat will
pass from the hotter to the colder as long as any dif-
ference of temperature exists.
Difference of potential in electricity is there/ore
analogous with difference of pressure in gases, with
difference of level in liquids, and with difference of
temjjerature in heat.
From what has been said, it follows that if two
conductors of the same material be in electric connection
with one another, and if no current be flowing from one
to the other, the potential of the two bodies must be the
same. Hence the potential at all points of a conductor on
which electricity is at rest must he uniform.
43. Volt. — If two conductors, having different electric
Chap. III.] THE VOLT. 87
potentials, be brought into the immediate neighbourhood
of one another, what is called 'Hnductive action" will
take place between them : that is to say, the presence
of each will disturb the distribution of electricity on the
other, and there will be an attractive force tending to
make the bodies approach one another. The magnitude
of this force is connected in a perfectly definite way
with the difference of potentials between the bodies,
their sizes and shapes, and their positions relatively to
one another, but this connection is in general a com-
plicated one. If, however, the opposed surfaces of the
two conductors be planes parallel to one another, this
force will be
4-508 X 10-i« X V2
— grammes
for each square centimetre of the opposed surfaces, where
V is the potential difference in '^ volts" between the
conductors, and d the perpendicular distance in centi-
metres between the surfaces.
If the force be measured in grains, the distance in
inches, and the unit of attracted area be one square inch,
then the force becomes
6-955 X 10-« X V^
In order that this formula may be rigorously true, it
is necessary that the bit of the plane surface on which
we are considering the attraction should be situated at a
distance from the edge of the plane which is large in
comparison with d.
The particular values of the constants employed in
the last two expressions have not been selected arbitrarily.
The selection of special units for the measurement of
force, distance, area, and potential difference determines
the values of the constants in each particular case, so
that while the first set applies to grammes, centimetres,
and volts, the second set applies to grains, inches, and
88
PRACTICAL ELECTRICITY.
[Chap. III.
volts. For a certain set of units of force, distance, area,
and potential difference (viz., dynes, centimetres, square
centimetres, and absolute electrostatic units of potential
difference), the constants become still simpler, and, indeed,
the magnitude of the electrostatic unit of potential differ-
ence was selected so as to make the fundamental equations
of attraction as simple as possible. This unit of potential
Fig. 29,
difference, however, is not used practically for several
reasons, one of which is that it is much too large for
such purposes ; hence, the equations just given, and
which are expressed in what are called engineer's units,
contain what, at first sight, might appear to be arbitrary
constants.
44. Measuring Potential Difference by Weighing.
— We can, therefore, measure the potential difference
between two conductors by weighing the attraction, and
Fig. 29 shows a rough lecture model of a ^^ weight electro-
Chap. III.] WEIGHT ELECTROMETER. 8§
meter " for effecting this result. A is a metallic plate insu-
lated from the ground, but in electric connection with any
conductor p, and therefore having the potential of P. B
is a plate suspended by fine wires from one end of the beam
of a balance which is well insulated from the ground, but
in metallic connection with c and d, and with a body Q.
B, c, and D have therefore the potential of Q. CD is
in reality a square or circular plate, with a hole cut in
it, which is nearly filled up by b, as seen in Fig. 30, the
distance between the outer edge of b
and the inner edge of c d being about
three-quarters of a millimetre, or 0-03 of
an inch. The use of the " guard ring"
as it is called, c D, is to cause the law
given above to be accurately true for all
parts of B when the lower surface of B is
in the same plane as the lower surface Fig. 30.
of c D (see the last paragi^aph but one,
page 87) ; and the instrument is so adjusted that when the
pointer points to nought on the scale, that is, when the
balance indicates the equality of the weight in the right-
hand scale-pan and the attraction of B, the lower surfaces
of B and c d are in one plane.
Such an apparatus can be used to measure a large
difference of potential absolutely in volts, and we might
define 2,000 volts as the difference of potential between
A and B when, the distance between A and b being half a
centimetre, and the area of b 100 square centimetres, the
force acting on b was 0*72128 grammes. As will be seen,
however, later on (^ 81, page 141), it is more convenient
to define a volt in terms of the ampere (the standard
of current) and the " ohm " (the standard of resistance).
Example 17. — If in the apparatus shown in Fig. 29
the suspended plate b were square, and its edge 1 -4 centi-
metres long, and if the distance between it and the fixed
plate A were 3 millimetres, what potential difference in
volts must be maintained between a and b so that the
attractive force may be 1 milligramme ?
90 PRACTICAL ELECTRICITY. (CTiap. HI
From what has preceded, we see that the attractive
force on each square centimetre of the area of the sus-
pended plate is
4-508 X 10-i«V2
0^32 grammes,
therefore the force on the whole suspended plate is
, ,, 4-508 X 10-i«y2
0^32 grammes,
and this, by the question, has to be equal to 0*001
grammes. Hence
_ 0-3 X 10^ / 0-001
/0-(
1-4 V 4-508
Answer. — 319*2 volts.
Example 18. — If the movable plate be circular, what
must be its diameter so that when at a distance of 1
millimetre from the fixed plate a difference of potentials
of 10 volts shall produce an attraction of yj^ gramme ?
Let X be the diameter of the circular movable plate in
centimetres, then its area equals
T'
Hence, as the potential difference is 10 volts, the
force is
wx" 4*508 X 10-i« X 10^
X ^ OO^ grammes,
and this is to be equal to y^^ ; therefore
x = 2 X 0*1 X 10* a/ —
V TT X 4*508
Answer. — 53*14 centimetres.
Example 19. — If the suspended plate be 3*5 square
centimetres in area, what must be its distance from the
Chap, ni.] SENSIBILITY OF A WEIGHT ELECTROMETER. 91
fixed plate so that 120 volts may produce an attraction of
^^ gramme *?
If X be the distance,
4-508 X 10-i« X 1202 1
3-5 X
x^ 500
.-. «= 120 X 10-5 ^3-5 X 4.508 X 500
Answer. — 1 '066 millimetre.
Example 20. — What force will be produced on a
movable plate of 4*3 square centimetres 4 millimetres
distant from the fixed plate, if the potential difference be-
tween them is 75 volts'?
Answer — 0*06816 milligrammes.
45. Increasing the Sensibility of the Weight Elec-
trometer by using an Auxiliary High. Potential. —
It would be, however, quite impossible with such an apparatus
to measure a potential difference of one or two volts, since unless
the distance between the plates was very small — in which case want
of perfect parallelism of the plates would introduce a serious error
— the force of attraction even with a fairly large suspended plate
would be extremely small. By emplojdng the following device,
however, the distance between the plates may be several milli-
metres, and the force of attraction some grains when a potential
difference of one or two volts between the bodies p and q (Fig. 29)
has to be measured.
Let the fixed plate a be charged permanently to a very high
and constant potential, V volts, by being connected with a body r
which is at that potential, Y being measured relatively to a metallic
case (not shown in the figure) which encloses the apparatus. First
let the suspended plate b and the guard ring c d be connected with
one of the bodies p, having a potential Vj, in volts, relatively to the
case of the apparatus, then if /i is the force in grains when the
suspended plate of area a square inches is in the plane of the guard
ring, and at a distance d inches from the fixed plate,
/i zr 6-955 X 10-9 X --^^'
From this equation it will be seen that even if /j is larger than
it was when p and a were connected with a and b respectively, d
may now be very much larger than the distances previously em-
ployed to separate the plates, since V - Vi is very great compared
with vx.
92 PRACTICAL ELECTRICITY. [Chap. IIL
Next connect o, with the suspended plate b and the guard ring
c D, then if the potential of q be v^ volts relatively to the outside of
the apparatus, and if /2 be the attraction ingrains for the same dis-
tance d between the plates,
/»= 6-955 X 10- x^i^'.
Hence
Y-v^-(V- vi) or vi -va = ,_ . (-v/TT- '^A)-
-v/6-955x 10-«xa^
If /i and /a be measured in grammes, d in centimetres, and a in
square centimetres, then reasoning in the same way, we obtain
Of course ^/f^ — ^/f^ will be no larger than would have been the
square root of the force of attraction if p and a had been respectively
connected simply, one with the fixed plate a, and the other with the
movable plate and guard ring, and if the high potential of k had
not been used ; but/j and /2, the two forces, will be each large, and
can be accurately measiu-ed, and what is especially important, d
will be large, and the error arising from want of perfect parallelism
of the plates entirely eliminated.
Another and simpler method of using the preceding apparatus
consists in keeping the attractive force constant, and in varying, by
means of a micrometer screw, the distance between the fixed and
movable plates, so that this constant force (which must of course
be known in grains or grammes) is exerted between the plates
when the lower surface of the movable one is in the same plane as
the lower surface of the g-uard ring. If then dx and d^ be the
distances in centimetres respectively when the same force / in
grains is produced when b is connected respectively with p and q,
A being connected with r,
y=6-956xl0-^i^^".
6-956 X 10'» X a
livi — Vi is very small, so also will be d^- tfj, but (?j and d^ will
Chap, in.] Thomson's electrometers. 93
themselves be large, so that no error will he produced on account of
want of perfect paraUelism of the fixed and movable plates.
Two electrometers on this principle have been invented by Sir
William Thomson; in the one, the ^^ absolute electrometer,'' the
force exerted on the movable plate b (Fig. 29) is known in grammes
or grains, so that the potential difference is measured absolutely in
volts ; in the other, the ^^ portable electrometer^'' the value of this
force is not known, but it is always the same when the lower sur-
face of the movable plate b is in the same plane as the lower
surface of the guard ring c d. With this latter arrangement we
cannot determine a potential difference Vx - v<i absolutely in volts,
but we can use the instrument as a relative electrometer, and
measure the ratio of Vy to v^ by taking a third or earth reading,
obtained by reducing the potential of a b to nought by connecting
it to the metallic case of the instrument : then if d^ is the distance
in inches between the fixed and movable plates,
f— 6-955 X 10-9 -^-^^ gi-ains.
a (V- 0)2
di
Combining this with the two other equations for/, we have
Vi — 0 = (<?i - <?•
6-956 X 10-9 X a
6-955 X 10-9 X a
Vi _ di - d^
V2 d^ — d^
"With Sir William Thomson's absolute and portable
electrometers, a potential difference of one volt can just
be measured.
A far more sensitive relative electrometer , but one
which is not at all portable, as hitherto constructed, is
Sir William Thomson's " quadrant electrometer,^^ which
owes its great sensibility to the fact that, unlike the last
two instruments, the sensibility of the quadrant electro-
meter is increased by increasing the potential of the
auxiliary electrified body. The quadrant electrometer in
its most perfect form is too complicated an instrument
to be employed by a beginner, but a description of the
details of the construction of a simplified type is given
in§ 75, page 130.
94
PRACTICAL ELECTRICITY.
[Chap. in.
46. Rough Electrometer. — A ^^ gold-leaf electrosGoj)e^*
is a rough electrometer or potential difference measurer.
This instrument, as generally made, has a variety of de-
fects, which will be referred to later on, but a form devised
by the author, and in which these defects are eliminated,
is shown in Fig. 31. It consists of a glass shade G G
resting on a wooden
base, and covered inside
with strips of tin-foil T
so as to leave only suffi-
cient of the glass bare to
enable the gold-leaves to
be visible. These strips
of tin-foil are bent round
the bottom of the glass
shade, and connected
electrically with a brass
ring round the bottom
of the outside of the
shade. To this ring
three horizontal brass
legs are attached for
fixing the shade to the
base, and in one of them
is a binding-screw s for
holding any wire which
we wish to electrically
connect with the tin.
Fig. 31. foil coating. Inside the
shade g G, a thin rod
of flint-glass g g, shaped as shown, is cemented into
two holes in the base, and at the centre of this rod is
cemented a little metallic tube t t^ carrying a thick wire
w w, and the gold-leaves l. This wire w w passes
through the top of the instrument without touching it,
and may carry at its top a little knob or a little binding-
screw, v is a vessel containing pumice-stone soaked in
strong sulphuric acid, which has the effect of keeping the
Chap. in.l GOLD-LEAF ELECTROSCOPE. 96
interior, and consequently the glass rod g g, quite dry.
When the instrument is not in use, the little ebonite
stopper py sliding a little stiffly on the wire, is pushed
down, and so closes the hole in the top of the instrument.
47. Action of a Gold-leaf Electroscope. — It has
been stated (§ 43, page 87) that when two conductors in
the immediate neighbourhood of one another are at
different potentials they tend to approach one another
with a force which depends solely on the potential dif-
ference, and on the shape and relative position of the
conductors. Hence it follows that when the gold-leaves
and the tin-foil coating of the electroscope are at different
potentials, there will be for each potential difference a
certain definite force pulling each gold-leaf towards the
tin- foil coating on its own side. This causes the gold-leaves
to diverge, and consequently to be slightly raised until
the forces due to their weight exactly balance the forces
of attraction between them and the tin-foil coating.
For a given gold-leaf electroscope, then, the di-
vergence of the gold-leaves depends simply on the poten-
tial difference between the gold-leaves L, and the tinrfoil
coating T ; and the value of any particular divergence
of the leaves, noted on a fixed graduated scale attached
to the electroscope, but not shown in the figure, can
be ascertained in volts for any particular electroscope
by comparison with a weight electrometer previously de-
scribed, or it can be calibrated by the method described
in § 191, page 354.
Experiment shows that a well-made electroscope,
with the leaves made of thin pure gold — not " Dutch
gold," which is often employed for this purpose — will
show a perceptible divergence for a potential difference of
about 100 volts.
If w w be connected with the screw s by means of a
piece of wire, no difference of potentials can be set up
between the gold-leaves and the outside, hence no diver-
gence of the gold-leaves can be produced even by putting
ihe electroscope on an insulating stand, and charging it
96 PRACTICAL ELECTRICITY. (Chap. III.
SO that sparks can be drawn from any part of the electro-
scope on the finger being approached.
If the wii'e w w be connected with any body A, and
the binding-screw s with any body b, then the divergence
of the gold-leaves serves to show the potential difference
between a and b in accordance with the absolute cali-
bration curve of the particular instrument. If then b
be a gas- or water-pipe in connection with the earth, the
potential of the tin-foil coating will be nought, and the
divergence of the gold-leaves will measure simply the
potential of a.
In a moist country like England the divergence of the
gold-leaves will approximately measure the potential of
w w, or of any conductor electrically connected with w w,
relatively to the earth without connecting s with the
earth by means of a wire, since the film of moisture which
condenses on the dusty wooden base makes a more or less
good electric connection between s and the ground, so
that, unless special precautions be taken to insulate the
wooden base from the ground, the tin-foil coating may
be regarded as being approximately at the potential of
the earth.
48. Objections to the Ordinary Methods of Con-
structing Gold-leaf Electroscopes. — In the gold-leaf
electroscopes commonly met with in shops, the rod w w,
carrying the gold-leaves L, is supported from the top of
the instrument, as if the sliding-plug p (Fig. 31) were
permanently kept pressed down, and the glass rod g g
removed. The consequence is that there is a great
tendency for electricity to leak down the outside of the
glass shade, on account of the moisture and dust on it.
And farther, even if the inside of the glass shade were
clean and dry, and had no tin- foil pasted on, much more
electricity would leak along its surface than would leak
along the surface of the thin flint-glass rod g g. For the
breadth of the surface at right angles to the direction of
leakage is much greater in the case of the shade than in
the case of the rod, or simply the width of the road
Chap. III.] FAULTS OF GOLD-LEAF ELECTROSCOPES. 97
along which leakage takes place is much greater for the
surface of the glass shade than for the surface of the rod.
To avoid this leakage, it is the practice of electrical
instrument makers to endeavour to render the surface
of the shade as insulating as possible by coating it with
shellac varnish, which is less hygroscopic, or attractive
of moisture, than the glass, and by not using any tin-foil.
But the effect of rendering the glass shade insulating is
to cause some conductor outside the instrument (the
table, or the walls of the room, or it may be the body of
the experimenter) to replace electrically the tin-foil
coating T seen on the glass shade in Fig. 31. Hence,
the gold-leaf electroscope, when constructed of the form
usually met with in shops, measures when dry the dif-
ference of potentials between the gold-leaves and some
vague body outside the apparatus. And whenever we
use it, we are landed on the horns of a dilemma — if we
leave the outside of the shade damp (as it frequently will
be in England unless it be dried near a fire), the potential
of the outside of the glass becomes practically that of the
earth, and the indications of the instrument have a
definite meaning. But the insulation of the glass being
much lowered by this coating of moisture, the mere con-
necting of any charged body by a wire with the knob of
the electroscope tends to discharge the body, or lower its
potential. On the other hand, if we take precautions to
clean and dry both surfaces of the glass shade, this
leakage difficulty may be overcome, but then a most
serious vagueness is introduced as to which of the
various conductors outside the electroscope is the one
with whose potential the potential of the body under
test is being compared. (See § 57, page 108.)
49. Conduction and Induction. — A conductor can
be electrified either by a transfer of electricity between
it and another conductor, or merely by an alteration in
the distribution of the electricity on its surface without
any transfer of electricity to another conductor. In
the former case the body is said to be electrified **hy
H
98 PRACTICAL ELECTRICITY. [Chap. Ill
conduction" or " conductively ; " in the latter " by in-
duction" or " inductively.*' Loading or unloading a ship
would be analogous with electric, conduction, while shift-
ing some of the cargo from the bow to the stern would
be analogous with induction. Acting inductively on a
charged insulated conductor neither increases nor dimi-
nishes the charge on the conductor as a whole, although
it alters the distribution of the charge (see 1 — 7, § 69,
page 123). If the conductor be previously uncharged,
then acting inductively on it produces no charge on it as
a whole, but merely induces equal and opposite charges
on its two sides or ends {see 8, § 69, page 124). An in-
ductive method may, however, be conveniently employed
to charge a conductor by connecting it with the earth
by a wire, while an electrified body is held near it, then
removing the earth connection, and lastly, the electrified
body. If this electrified body has a positive potential,
the charge induced in the conductor will be nesfative.
Instead of connecting the conductor with the earth by a
wire, one's own body may be used, and the conductor
touched with the finger.
When the gold-leaves of an electroscope are charged
inductively in this way, care must be taken not to in-
duce too great a charge in the knob, as otherwise on
removing the electrified body, the leaves will diverge so
widely as to be torn asunder.
50. Potential Uniform at All Points Inside a
Closed Conductor. — We have seen that when electricity
is at rest on a conductor the potential at all points of the
conductor is the same. The following experiment will
show that not only is this the case, but that the potential
at all points inside a closed hollow conductor is uniform,
and has the same value as at any point on the surface of
the conductor: — Attach one end of a fine wire to the
knob of the electroscope, and the other to the end of
a clean dry glass rod, which is to be used as an insulating
handle for holding the end of the wire by. Then, if this
end be touched against the outer surface of a conductor,
Chap. III.J NO FORCE INSIDE A CLOSED CONDUCTOR. 99
charged conductively or inductively, or, after being intro-
duced inside the conductor through a hole in its surface,
it be first touched against the inside surface, and then be
held merely inside the hollow conductor without touch-
ing it, or be moved about inside the hollow conductor,
the divergence of the gold-leaves will be exactly the
same, proving what is stated above. The hole in the
surface of the conductor through which the test wire is
introduced may be fairly large — as large, for example, as
the opening at the top of a cofiee-pot — without altering
what has just been stated, excepting for points in the air
just inside the pot close to the opening, where the
potential will be somewhat different from the uniform
potential inside the pot. If, however, the opening be
small, then the potential even just inside the opening
will he found to be the same as the uniform potential of
the pot, so that if the metallic surface of the conductor be
not continuous, but be made of wire gauze, or even of
hits of wire like a bird-cage, the potential is found to be
uniform inside, unless the meshes of the wire gauze be
very large.
51. No Force Inside a Closed Conductor Due to
Exterior Electrification. — Since the potential at all
points inside a hollow closed conductor is uniform and
equal to the potential of the surface of the conductor, as
far as exterior electrification is concerned, it follows that
if there be electrified bodies inside a hollow conduc-
tor, either some or all insulated from the conductor, the
raising or lowering of the potential of the conductor
relatively to the earth will not alter in the slightest the
potential difference between any two bodies inside. Fn
fact, no matter what electrified bodies there may be in-
side the conductor, the relative internal distribution of
potential will be quite unaffected by electrifying the con-
ductor outside, either conductively or inductively. This
experiment was first tried by Faraday on a large scale ;
he found on taking his most delicate electrical appa-
ratus inside a room which he had had built of wood
100
PRACTICAL ELECTRICITY.
[Chap. III.
twelve feet cube, covered with tin-foil to make it con-
ducting, and insulated so that it could be charged, that he
was totally unable to deteci the slightest evidence of this
room being electrified outside, even when it was so power-
fully electrified that sparks were being given ofi* by the
walls of the room, nor could he detect any evidence of
any electric disturbance
produced outside the
room. This important
fact may be expressed
by saying that there is
no electric force inside a
conductor due to exterior
electrification, or a me-
tallic shell, no matter
how thin, completely
screens inside bodies
fronn exterior electrifica-
tion.
This fact may be
tried experimentally,
thus— C c (Fig. 32) is a
cage made of rather fine
wire gauze, and sup-
ported on an insulating
stand. Inside this cage
^ are suspended one pair
of pith balls, by means
of silk fibres, which are
fairly insulating, and
one pair by pieces of cotton, which is relatively a fairly
good conducting substance. Outside the cage one or
more pairs of pith balls are suspended by pieces of
cotton. Then it will be found that, whereas the pith
balls outside the cage can be made to diverge from
one another, either by bringing an electrified body near
the cage so as to electrify it inductively, or by giving
it a charge, it is impossible by any method to produce
Fig. 32.
Chap. III.] METALLIC BOX NOT A MAGNETIC SCREEN. 101
the slightest divergence of either of the pairs of the pith
balls inside the cage.
The converse of this, however, is not universally
true, that is, a metallic box may or may not screen
bodies placed outside it from the action of an electrified
body put inside the box. Four distinct cases must be
considered.
1. If the box be connected with the earth the
screening action will be perfect whether the box be small
or large.
2. If the metallic box be not connected with the
earth, and be not much larger than the electrified body
inside it, the screening action will be very small.
3. If the box be not connected with the earth, but
if the dimensions of the side, which is between the body
inside it and the body outside, be fairly large compared
with the distance between the bodies, the screening action
will be considerable.
4. If the dimensions of the side referred to in 3 be
very large, then the screening action will be as perfect
as with arrangement 1.
52. A Metallic Box not a Magnetic Screen unless
made of Very Thick Iron. — Contrasted with the ex-
periment made with the apparatus shown in Fig. 32,
the following may be tried : — b b (Fig. 33) is a wooden
stand covered with a glass shade, and having inside it a
small magnetic needle m^ suspended by a fibre of unspun
silk from a fixed wire bridge. Attached to the needle is
a long pointer j9 jt?, by means of which the deflection of
the needle is read ofi" on a scale fastened at the base of the
instrument. The magnetic needle takes up a particular
position due to the earth's magnetic attraction, from which
it may be deflected by means of the magnet m, which can
be fixed in any desired position. If, now, when the
needle m has been deflected 30° or 40° from the position
it occupied due to the earth, screens of copper- wire c c,
brass wire b 6, &c., be successively put over the stand and
glass shade b b, and thus interposed between m and m, it
102
PRACTICAL ELECTRICITY.
[Chap. III.
will be found that not the slightest change will be produced
in the deflection of 7n, or, in other words, the insertion of
these screens does not in any way diminish the magnetic
attraction between m and m. And- this will be found to
be still the case even when a screen made of iron wire is
In making this latter experiment it is some-
times found that the interposition of a screen made of
iron wire does vary the deflection, but on examination it
will be found that this variation is due to the iron wire
itself having been previously magnetised, and having
Fig. 33.
retained some of its previous magnetism from its being
hard, and not to its shielding m from m. The proof of
this is that turning round the screen will alter the deflec-
tion of 7?i, and hence that, while with one position of the
iron screen the deflection of m is diminished, with another
it will be much increased. This disturbing efiect arising
from residual magnetism on the screen, can be avoided
by constructing the screen of soft iron wire, and making
it red-hot just before the experiment.
If, however, a wide plate of thick soft iron be in-
serted between m and m, the deflection of m from its
position due to the earth's magnetism will be diminished,
and if B B be inserted inside an iron box, whose sides
Chap, III.] MARINE AND REFLECTING GALVANOMETERS. 103
have the thickness of the sides of an ordinaiy iron safe,
then not merely will this box screen m from the action of
M, but alscrfrom the earth's magnetic action.
53. Marine Galvanometer. — This plan of screening
a suspended magnetic needle from outside magnetic attrac-
tion, by inserting the former in an iron box with very
thick sides to it, has been employed by Sir W. Thomson
in his *' marine galvanometer^'^ an instrument intended to
be used on board steam-ships, where the motion of the
large masses of iron composing the engines, the shaft of
the screw, &c., would seriously disturb the deflection of
an ordinary unshielded galvanometer. Oscillations of
the needle that might be produced by the rolling of the
ship are avoided by suspending the needle by a tibre
attached above and below, and passing through the
centre of gravity of the needle, as described in § 27,
page 60.
54. Reflecting Galvanometers. — With the marine
galvanometer, and generally with all Sir W. Thomson's
Fig. 34.
galvanometers, a very small deflection of the needle can
be observed without the employment of a long pointer
(which would be unwieldy, and by adding to the mo-
ment of inertia of the suspended arrangement, would
render the needle sluggish), as well as without the em-
ployment of a microscope, by the reflection of a ray of
light from a small piece of looking-glass fastened to the
104
PRACTICAL ELECTRICITY.
[Chap. III.
magnetic needle, and turning with it. In Fig. 34^ s is the
mirror, reflecting a ray of light from a lamp on to a scale
t, shown more in detail in Fig. 35, the double convex
lens L being for the purpose of making an image of the
slit m 771, on the scale t, which could not be done by
a pla7ie mirror s, as shown in the figure. To avoid the
direct light of the lamp producing a general illumination
Fig. 35,
of the scale, and' preventing the reflected image being
clearly seen, the lamp is sometimes shut up in a box as
shown, but a complete box is not absolutely necessary, the
mere front of the box, as seen in Fig. 36, being suflicient
to keep off" direct light.
The handle s (Fig. 35) works a rack and pinion for
moving the scale horizontally, so as to bring the zero
mark on the scale opposite the spot of light or image. If
a slit mj, m2(Fig. 35) alone be employed, it must, of course,
be made very narrow so as to obtain a sharp line of light
on the screen ; but a better plan is to use a wide slit, or,
Chap. III.]
SCALE AND LAMP.
105
rather, a round hole, and to stretch a fine wire across it
vertically, the image of this wire on the screen, and iiot
the edges of the spot of light, being used to read by. Be-
cause not merely can the spot of light be large, in which
case the numbers on the graduated scale can be easily
seen by it, but any flickering of the flame, produced by
a draught, although causing the spot of light on the scale
to flicker in a corresponding manner, does not produce
any flickering of the image of the wire.
Fig. 36.
An objection to the use of a plane mirror s and the
lens L, is that the image on the scale is necessarily very
much larger than the object, and hence not nearly as well
illuminated. A better plan is to use a concave mirror,
with which an image can be formed on the scale without
the use of a lens at all, the distance between the lamp and
the mirror being then equal to the radius of the mirror.
But, perhaps, the best method is that due to Mr. Mud-
ford, a former student of the Finsbury Technical College,
which consists in using the concave mirror and putting a
double convex lens l l between the wire w and the flame f,
as shown in Fig. 36. With this arrangement a good
106
PRACTICAL ELECTRICITY.
[Chap. 111.
image is obtained with a comparatively small flame. The
lens should be placed close behind the wire, and the flame
should be at about the principal focus of the lens, so that the
efiect is to produce a general illumination
of the lens, which is found to give very-
good results if it has a focal length of
about four inches. Instead of a wire,
Mr. Mather has found that a vertical
scratch on the lens produces a very good
image, and may be employed instead of
the wire placed just in front of the lens.
A paraffin lamp, with an ordinary flat
flame, is commonly employed with reflect-
ing instruments, the edge of the flame
being turned towards the lens ; but a gas-
jet, shown partially in section in Fig. 37,
and constructed by Mr. Mudford, may be
conveniently substituted for the paraffin
lamp. To obtain a fairly intense light,
this bui'ner is constructed on the regene-
rative principle, that is, the air is heated
before coming in contact with the flame.
This result is obtained by having no
opening for the air at the bottom, and
causing it after entering the holes H to
pass down between the outer cylinder J j
and the hot inner cylinder c c^ at the
bottom of which a ring is cut away to
^^^y^^^^^ff allow it to get to the flame. The ray of
Pig. 37. light passes out through a small disc of
glass at T, and to avoid the glass being
blackened by the flame being accidentally turned up too
high, the burner should be governed, a Suggs's two cubic
feet steatite float burner answering well for this purpose.*
55. Angular Motion of the Reflected Ray is Twice
the Angular Motion of the Mirror. — Let i o (Fig. 38) be
* A flat albo -carbon bvirner with a special form of chimney has
also been used by the author with good results.
Chap. III.] MOTION OF MIRROR AND REFLECTED RAY. 107
the incident ray, and or, or' the reflected rays when the mirror
is in the positions s s and s' s' respectively. Let o p, o p' be per-
pendicular to the mirror when it is in these two positions. Then
by the law of reflection,
angle i o p =: angle r o p,
and angle i o p' =: angle r' o p' ;
therefore, subtracting the first from the second, w0 have
angle p' o p ±: angle r' o li — angle p' o p,
or angle r' o r = 2 angle p' o p ;
but r' o R is the angle through which the reflected ray is deflected,
and p' o p is the angle between the perpendiculars to the mirror in
its two positions, and is, therefore, the angle through which the
mirror is turned ; hence, when a mirror is turned through any angle^
the reflected ray turns through twice that angle.
56. Connection bet"ween the Motion of the Image on
a Plane Scale and the Angular Deflection of the Mirror.
— Let the mirror be parallel to the scale when no current is passing,
and let the image be reflected to r and r' for currents c and c' re-
spectively ; then, since the deflection of the magnet in a mirror
galvanometer is always small^ and since we have seen (§ 20, page
46) that for small deflections the current is always proportional
to the tangent of the deflection, no matter what be the shape of
the coil or the shape or size of the needle, provided its magnetic
axis is parallel to the plane of the coil when no current is passing,
itfoUowsthat (Fig. 38)
C : C : : tan.
108 PRACTICAL ELECTRICITY. [Chap. Ill
y/ 1 + tan.'-' I o R— 1 .y/ 1 -f tan.2 io r^— 1
tan. I o R ' tan. i o r'.
IB.
IR'
01
OI
Hence, when i r and i r' are nearly equal, we may say that
-7 = — , approximately,
but for very accurate ohservations this approximation must not be
employed.
57. Static Electrical Apparatus should be Enclosed
in a Metallic Case. — In constructing static electrical
apparatus, we must carefully consider what are the ac-
tions we wish to take place, and what to avoid ; for ex-
ample, in the case of a gold-leaf electroscope we wish the
divergence of the gold-leaves to measure the potential
difference between one conductor attached to the knob
w (Fig. 31), and another attached to the screw s. If, then,
w and s be joined by a piece of wire so as to be at the
same potential, we wish that no divergence of the leaves
shall be able to be produced either by electrifying the
electroscope as a whole conductively, or by electrifying
it inductively by bringing a charged body near it. And
it will be found, if the tin-foil coating t cover nearly
all the glass shade, only just sufficient space being left
without tin-foil to see the gold-leaves through, that it is
impossible in any way to produce a divergence when w is
electrically connected with s ; whereas, if there be not in-
foil, or if the tin-foil only cover a portion of the shade,
that a divergence of the leaves can be easily produced.
Want of care in this particular prevented Piazzi
Smyth from being able to determine, by his experiments
on atmospheric electricity, made on the Peak of Teneriffe,
even whether this electricity was positive or negative.
Chap. III. J QUANTITY OF ELECTRICITY. 109
58. Quantity of Electricity. — We have seen that it
is possible to electrify a non-conductor, such as ebonite,
by rubbing it with a piece of dry clean flannel, and ex-
periment shows that it can be either highly electrified by
a prolonged rubbing, so that the gold-leaves of the elec-
troscope diverge widely when the ebonite is held at a foot
or two away from the knob of the electroscope, or it may
be only slightly electrified by being only just touched
with the flannel, in which case the ebonite may be
brought quite close to the knob, or may even be made to
touch the knob, without any perceptible divergence of the
leaves being produced. The rubbed ebonite may, there-
fore, be said to possess a greater or smaller ^' electric
cliarge^^ or the " quantity of electricity " in the ebonite in
the first case may be said to be greater than in the second.
Strictly speaking, however, as we have no conception of
the existence of electricity apart from the body which is
said to be electrified (as we have of a pint of water apart
from the pint pot), it is more correct to speak of the
" amount of a hodys electrification " than of its charge of
electricity, or of the quantity of electricity in it. But
just as it is very convenient to speak of an electric current,
as if it had an independent existence apart from the con-
ductor through which it is said to be flowing, so it is
Fig. 39.
convenient to speak of a charge, or a quantity of elec-
tricity, as if electricity existed independently.
In order to decide what we mean by saying that one
quantity of electricity is two or three times as great as
another quantity, or simply one quantity is two or three
110 PRACTICAL ELECl'RICITY. [Chap. IH.
times another, we shall adopt the following arbitrary
definition : —
When one conducting body A is entirely surrounded by
another conducting body b (Fig. 39), the quantity of elec-
tricity in A, or the electric charge in A, is directly propor-
tional to the potential difference between A and b as long as
the position of K, relatively to b, is absolutely fixed.
For example, if A be an insulated conducting body
suspended in a room b, the walls, ceiling, and floor of
which are made of conducting material, then the quantity
of electricity on A is directly proportional to the potential
difference between A and B as long as the position of A in
the room is unaltered.
If not only a be inside the room b, but if in addition there be
another electrified body c fixed in position in the room, as in Fig. 1 34,
page 341, it can be shown that, if the potential difference between a
and B be represented by a b, and the potential difference between
c and B be represented by c b, the total charges on a and on c may
each be regarded as being composed of two parts — the total charge
on A being equal to the charge a would have if the potential differ-
ence between it and b were a b, and c were connected with b, plus
the charge a would have if it were connected with b, and if
the potential difference between c and b were c b, c being now, of
course, insulated from b. Also the total charge on c is the charge
c would have if the potential difference between it and b were c b,
and a were connected with b, plus the charge c would have if it
were connected with b, and the potential difference between a and
B were ab, a being now, of course, insulated from b.
If, however, A be moved about inside b, then the
potential difference between a and b gives us no indica-
tion of the relative charges on A. Or, again, even if a
and c be at rest inside b, the potential differences be-
tween A and B, and between c and b, give by themselves
no idea of the relative amounts of electricity on a and
on c. In exactly the same way, although the prennure of
gas in a given vessel, at a constant temperature, is pro-
portional to the weight of gas in the vessel, the pressure
of gas in a vessel whose temperature is varied in some
unknown way, or the pressures of the gas in different
vessels of unknown volumes, give no indications of the
Chap. III.] QUANTITIES OP ELECTRICITY COMPARED. Ill
various weights of the gases. The height of the baro-
meter, for example, tells us, by itself, nothing about the
total weight of air in the room.
59. Comparison of Quantities of Electricity. — In
order that the indications of a difference of potential
measurer may be directly proportional to the charge on
a body connected with it, or rather to the charge od
the body in excess of what it might have inductively
when its potential is nought, the body must be fixed in
size and shape, and in its position relatively to other
bodies. So, in the same way, in order that the indica-
tions of a pressure gauge may be directly proportional to
the weight of a gas, it is necessary that the vessel con-
taining it should be fixed in size and kept at a constant
temperature. In order, therefore, to compare the weights
of the same kind of gas in different vessels at different
temperatures by means of measurements of pressure, we
must first equalise the temperatures^ and then succes-
sively entirely empty the gas in each vessel into a
standard vessel, and measure the pressure that each of
the quantities of gas, when put into the standard vessel,
will produce by itself.
To empty all the gas out of a vessel into a standard
gas-holder, to which the pressure gauge is attached, for
the purposes of thus ascertaining the weight of gas in
the first vessel, would be an extremely difficult and in-
convenient process ; whereas, to empty all the electricity
out of a body into a standard body, attached to an elec-
troscope, is an extremely simple one. Because, since there
is no electricity at the bottom of the inside of a conduct-
ing pot {see § 64, page 118), it follows that if a charged
body be put inside a conducting pot and touched against
the bottom,. it will give up all its charge to the pot, and
when drawn out, without touching the sides of the pot,
will be found to be completely discharged.
Hence, using this principle, we can, with the appa-
ratus shown in Fig. 40, compare the electric charges that
are given, say, to the metallic bodies b, b, when hung up
112
PRACTICAL ELECTRICITY.
[Chap. III.
by their silk cords, and charged, say, to the same poten-
tial. All that has to be done is to put first one of them
inside the insulated tin-pot P, touch it against p near the
bottom, and observe the divergence d^, of the gold-leaves
rig. 40.
of the electroscope. Then, after withdrawing the first
body and discharging the electroscope, place the second
one in the metal pot p, touch it, as in the case of the
other body, near the inside of the bottom of p, obtaining
a divergence of the gold-leaves, say dc^^. Then d^ and d<^
will, according to the proper calibration curve of the
electroscope, measure the potentials of the pot p in the
Chap. III.J QUANTITIES PRODUCED BY RUBBING. 113
two cases, and hence will measure the relative quantities
of electricity on the two bodies b.
From what has been said it will be seen that if either
of the bodies had touched p on the outside, this result
would not have been obtained ; also that we must not, for
example, stand close to p when making the first mea-
surement, and not close to p when making the second,
since the essence of the test is that the charges on the
two bodies b shall be successively entirely transferred to
the conductor p, and that p shall be absolutely fixed in
external shape and in position relatively to other bodies.
Further information regarding the unit of electric
quantity, and more exact modes of measuring quantities of
electricity, will be found in Chapter VII., § 155, page 289.
60. Quantity of Electricity produced by Rubbing
Two Bodies Together. — On putting the insulated
charged body b, in the last experiment, into the pot p,
it is noticed that after B has been lowered so far into the
pot that it is well under cover of the sides {which occurs
vihen B cannot he easily seen from outside), no further
increase is produced in the divergence of the gold-leaves
by further lowering B, or even by touching b against tJie
sides or bottom of the pot. Hence, in order to measure
the charge on a body, it is not absolutely necessary to
discharge that body into p, since experiment shows that
the potential of p remains the same whether b is dis-
charged into P, or whether b is merely well inside p.
The fact is that as soon as b is well under cover of the
sides of p, there is, as was first shown by Faraday, a
charge induced on the inside of the pot p, exactly equal
to the charge on b, but of the opposite sign, and another
charge on the outside of tlie pot, also equal to the charge
on B, but of the same sign. This latter charge remains
unaffected by touching b against the pot, as this has only
the effect, if b be a conductor, of allowing the charge on
B to neutralise the charge which has been induced on
the inside of the pot equal to that on B, but opposite in
sign.
X
114 PRACTICAL ELECTRICITY. [Chap. in.
This important fact that, as soon as B has been
lowered a certain distance into the pot, the potential of
the pot becomes equal to what it would have been if all
the charge on B had been given up to the pot, enables us
to measure the charge on an insulator, which charge
could not easily be all communicated to P, even on
touching the insulator against p.
Consequently this apparatus may be conveniently em-
ployed for testing the amounts of positive and negative"
electricity that are simultaneously produced when two
bodies are rubbed together, e and f (Fig. 40) are re-
spectively discs of ebonite and of wood, the latter being
covered with cat's-fur. The ebonite is a good insulator ;
the cat's-fur and wood make but poor insulators; both discs
are, however, as seen in the figure, mounted on long, thin,
insulating glass handles. If, now, the glass handles be
cleaned and dried, and if the ends of them be held in the
hands, the two discs may be rubbed together without prac-
tically any of the charge of electricity produced in the ebo-
nite or in the cat's fur being lost. When either of these
discs is held inside the metal pot p, it is found that the gold-
leaves will diverge ; but there is this difference between
the divergence that, whereas when the divergence is pro-
duced by the rubbed cat's-fur being held inside the pot,
this divergence can be increased by bringing either near
the pot, or near the knob of the electroscope, or near the
wire connecting them a piece of dry clean glass rod that
has been previously rubbed on dry silk, on the other
hand, if the gold-leaves are diverging because the
rubbed ebonite is held inside the pot, the divergence of
the gold-leaves is diminished by the approach of the
piece of rubbed dry clean glass. Hence, the electricities
are of the opposite sign, that on the rubbed cat's-fur being
like the electricity on rubbed glass, which, as already
stated in § 41, page 85, is called vitreous or positive,
while that on the rubbed ebonite is called resinous or
negative.
But more than that, experiment shows that if, by
Chap, in.] WHY RUBBING ELECTRIFIES. 115
means of the insulating handles, both the rubbed discs be
held well inside the pot, either both not touching the
pot, or both touching it, or one or other touching it, or
touching one another, the divergence of the gold-leaves
is absolutely nought. Hence we conclude that the charges
of electricity in tJie ebonite cmd cat^s-fur, which have been
rubbed together, are not only opposite in kind, but are
equal in amount.
Before trying this experiment it is well to make sure
that there is no residual charge of electricity in the ebo-
nite disc. This can be ascertained by seeing whether
any divergence of the gold-leaves is produced on insert-
ing the disc into the pot before it is rubbed with
the cat's-fur. If it is found that such a divergence is
produced, then the disc should be discharged by being
passed through the flame of a spirit-lamp before it is
rubbed with the disc of cat's-fur.
When this apparatus is not in use, the plug p at the
top of the electroscope should be pushed down to pre-
vent dust and moisture entering the electroscope; and
the two halves of the indiarubber stopper i should be
inserted in the neck of the glass bottle belonging to the
insulating stand, to prevent dust and moisture settling on
the glass rod of this stand.
61. Object of Rubbing Two Bodies Together to
Produce Electrification. — The sole object of rubbing
together the two bodies when one or both of them is
more or less a non-conductor, is to bring the various
parts of the surfaces of the two bodies successively into
intimate contact. The energy expended in the friction
is not only far greater than the electric energy developed,
but is in no way a measure of the latter. This may be
experimentally seen from the fact that if, after rubbing
a rod of ebonite with a piece of cat's-fur, the two be
brought together towards the knob of the electroscope
with the fur wrapped round the ebonite as it is during
the operation of rubbing, practically no divergence of the
gold-leaves will be observed ; whereas if the ebonite and
116* PRACTICAL ELECTRICITY. [Chap. HI
the cat's-fur be separated after being rubbed together,
the ebonite will* produce a marked divergence. In fact,
as will be more clearly seen later on (§ 189, page 352), the
electric energy stored up in the rubbed ebonite after being
separated from the fur is not the equivalent of the work
done in the rubbing, but of the small amount of work
done in the separation against the electric attraction of
the negative electricity in the eboiiite for the jjositive in
tlie fur.
If the bodies are both conductors, simply touching
them together without rubbing is all that is necessary
to produce the full electrification, and no increase in the
charges will be produced by rubbing the two bodies
Fig. 41.
together. Of course, if the bodies are conductors, one or
both of them must be held by insulating handles^ other-
wise the charges of positive and negative electricity re-
siding in them respectively during contact will flow
together through the body of the operator, and neutralise
one another on the conductors being separated.
'62. Proof- plane. — The preceding experiments for
measuring potential differences and the charges of elec-
tricity in bodies, must be carefully distinguished from
another experiment, with which the student is prob-
ably more familiar — viz., that of successively touching
various parts of the surface of a charged conductor with
a small disc of metal m fixed at the end of an insulating
handle h, shown in Fig. 41, and called a '■'' proof plane^^
and testing the various electric states of this proof-plane
by touching it against the knob of the electroscope each
time after it has been touched against some particular
part of the surface of the charged conductor.
Chap, in.] ELECTRIC DENSITY. 117
63. Electric Density. — What this experiment decides
is the various potentials of the proof -plane at the different
times when it is being touched against the knob of the
electroscope, and not the potentials of the various parts
of the surface of the conductor against which it has been
touched. The proof-plane when touching the charged
conductor has the potential of the conductor; and,
further, if when in contact with the conductor it be
pressed flat against the surface, the quantity of electricity
that was previously on the bit of the surface of the
conductor now covered by the i)roof-plane rests on the
surface of the proof-plane, instead of on the surface of
the conductor. When the proof-plane is removed by the
insulating handle, it will carry away with it the charge
of electricity, provided that in taking the proof-plane
away it be moved without tilting along a line per-
pendicular to the surface. But its potential alters as it
is being moved, so that while when the proof-plane is in
contact with the charged conductor, its potential, quite
irrespectively of the quantity of electricity that happens
to be on it, is simply that of the charged conductor, its
potential, but not its charge of electricity, varies as it is
moved ; and, finally, when the proof-plane has been
moved out of the influence of the charged conductor, and
is then put into contact with the knob of the electro-
scope, its potential becomes simply proportional to the
charge of electricity on it.
Hence the divergence of the gold-leaves, which (accord-
ing to the calibration curve of the electroscope) measures
directly the potential of the proof-plane, measures in-
directly the electric charge residing on it, and which
previously resided on that small hit of the surface of tJie
charged conductor that was covered up hy the proof-plane.
This quantity of electricity is proportional to the
" electric density ^"^ or the quantity of electricity residing
on a unit of area at that part of the surface of the
charged conductor touched by the proof-plane. And the
density is called positive or negative, according as the
118 PRACTICAL ELECTRICITY. [Chap. III.
charge taken away on the proof-plane is positive or
negative.
Experiments made thus with a proof -plane show that,
in the case of an electrified flat sheet of metal which is
far away from other conductors, the density is very much
larger near the edges than it is at points far removed
from the edges, and is less and less the farther the point
is from the edge. If, however, two flat sheets of metal
such as A and b (Fig. 29, page 88) be placed parallel to
one another, and near together, the density at miy point
on either of the opposed surfaces is found to be the
same in value, but is positive on the surface of one of
the plates and negative on the other. At points near
the edge of the upper surface of A the density will be a
little less than when it is nearer the middle of that surface,
but, if the potential of b and of the guard ring c D be
the same, the density at all points on the lower surface
of B will be absolutely the same.
In the case of a charged conically-shaped conductor,
such as is shown in Fig. 118, page 316, the density is very
great at the pointed end, and comparatively small at the
rounded end. The use of the special apparatus on which
the conical body is supported for enabling accurate ex-
periments on density to be made is described in § 171,
page 316.
64. Density is Nought on the Inner Surface of a
Closed Conductor. — Experiments made with a proof-
plane in the way just described show that the density is
nought on the inner surface of a nearly closed hollow
conductor, and even when the conductor is only partially
closed the density is found to be nought at any point on
the inner surface from which bodies outside the con-
ductor are not easily visible. For example, the density
on the parts near the bottom of the interior of a charged
metal cofiee-pot, or even on the parts near the bottom of
the interior of a charged shallow metal tea-pot with the
lid open, is practically nought, but will be no longer
nought if one end of a metal rod, say the end of a
Chap. III.] MODES OF VARYING POTENTIAL. 119
poker, be held inside the pot without touching it. And
not merely on the inner surface of a pot made of
continuous metal will the density be found to be nought,
but in the case of a pot made of wire-gauze, even with
fairly wide meshes, the density is also nought at all parts
on the inner surface except close to any very large
opening. But in this case, as in the other, if a metal
rod be held partly inside and partly outside the pot, the
distribution of density will be quite altered.
From the preceding experiments we see that electricity
at rest resides only on the surface of a conductor, an(v
therefore, as far as the effects of electricity at rest are
concerned, it is immaterial whether our conductors are of
solid or hollow metal or whether they be simply made of
wood and coated with tin-foil or gold-leaf.
65. Potential of a Conductor Depends Partly on
the Amount of Electricity on it. — This is easily seen
from the fact that the divergence of the gold-leaves can
be varied by charging more or less a conductor in electric
connection with them.
66. Potential of a Conductor Depends Partly on
its Shape. — That altering the shape of a conductor alters
its potential may be proved thus : — p (Fig. 42) is a metal
plate fixed to the wire w w of the electroscope in place of
the knob, and m is an insulated piece of metal carried by
a clean dry glass handle h, by means of which m may
be laid on p, or separated more or less from p. If now
M be laid on p, and a charge given to p and m as
one conductor, the leaves will diverge, indicating the
common potential of p and M ; and it will be found that
on sliding m over p, or tilting m up, without in either
case separating m from p, the divergence of the gold-
leaves diminishes. But on putting m back into its
original position, the divergence of the gold-leaves regains
its original value, proving that the alteration of the form
of the compound body M P, without altering the amount
of electricity on it, alters its potential.
67. Potential of a Conductor Depends Partly on
120 * PRACTICAL ELECTRICITY. [Chap. III.
its Position. — The fact that the potential of a conductor
can be changed by varying its position relatively to other
bodies can be proved also with the apparatus shown in
Fig. 42. If, M having been removed to some distance
from p, a charge be given to p, it will be found that
on approaching M, held by its insulating handle, towards
p, the divergence of the gold-leaves or the potential of p
Fig. 42.
diminishes. Further, if, when m is near p, m be con-
nected with the tin -foil coating of the electroscope, or
with the earth with which the tin-foil coating is already
connected, the divergence of the gold-leaves will dimi-
nish much more. And, lastly, if M, still in connection
with the tin-foil coating, be placed very near the plate p,
and parallel to P, but without touching it, the divergence
of the gold-leaves will be almost nought, showing that
the potential of p has practically become that of the tin-
foil coating, or nought. On removing m, the divergence
will regain its original value, showing that the potential of
Chap. Ill] MODES OF VARYING POTENTIAL. 121
p was diminished, not by p having been discharged (which
is also, of course, one way of diminishing its potential, and,
therefore, care must be taken that m does not touch p)
but by the mere approximation of the piece of metal M
connected with the tin-foil coating.
68. The Potential of a Conductor can therefore be
Varied by —
1. Altering the dmrge of electricity on it.
2. Altering the external shape of the conductor without
altering the charge of ehctricity on it.
3. Altering its position relatively to other bodies.
In the same sort of way the pressure of a gas (say
oxygen) in a gasometer can be varied by —
1. AlteHng the weight of the oxygen in the gasometer.
2. Altering the size of the gasameter without altering
the weight of oxygen in it.
3. Altering the temj)erature.
69. Examples showing the Difference between
Potential, Density, and Quantity; — To familiarise the
student with the difference between potential, den-
sity, and quantity, the following examples may be
considered, a (Fig. 43) is an insulated
piece of metal charged positively, and far
away from other bodies, so as to be beyond
the range of their inductive action ; then
its potential, the density on its two sides,
and the quantity of electricity, or charge
on it (the approximate modes for measur- Fig. 43.
ing which have been described, § 59,
page 112), are given in the following table; a positive
potential meaning that if the body were joined to the
ground by a wire, or "^^tt^ to earth" as it is technically
called, positive electricity would flow to the ground from
this body.
Now, let a large body b, in metallic connection with
the earth (Fig. 44), be brought near A on its right side,
then 2 will represent the electric state of A. Let b be
brought nearer to a ; a's state will now be given by 3.
122 PRACTICAL ELECTRICITY. [Chap. III.
If, on the other hand, A and b be separated more and more,
a's state will be more and more like that given in 1.
Next let a large positively charged body, c (Fig. 45), be
Fig. 44.
brought near A on its left side, 4 will then represent a's
state. Bring c nearer to a, but not so near that a spark
or a brush discharge * can pass between a and c ; a's state
Fig. 45.
will be changed to 5. Now, while c is near a, let a be
connected electrically with the ground (Fig. 46) ; positive
electricity will pass from a to the ground, and 0 will
* See notes to ^^ 192, page 358, and § 196, page 369.
Chap. III.] POTENTIAL DENSITY AND QUANTITY.
123
then be the potential, density, and charge of A. Lastly,
let A be disconnected from the ground, and then let c be
rcmoved to a great distance from A, when 7 will be
arrived at.
STATE OF THE CONDUCTOR A.
s
§!
Densitt.
^
^
Potential.
Charge.
■s
Eight side.
Left side.
1
43
+
+
+
+Q,say
2
44
+, but less than
ini.
-f-, but greater
than in 1.
-\-, but less than
ini.
before.
s
-\-, but small.
4", and much
greater than in i.
+, but much less
than in 1.
+ Q.
4
45
-}-, and greater
than in 1.
+, and greater
than in 1.
-+-, but less than
ini.
+ Q.
5
+, and still
greater than in i.
-}-, and much
greater than in i.
Almost nought.
+ Q.
6
46
Nought.
Nought.
—
— q,say
7
Negative.
Negative.
— , but less than
in 6.
— q as
in 6.
Bringing up the positively charged body c near the
body A in Fig. 45 has exactly the same sort of effect
as heating considerably the left end of an elongated
gas-holder, and slightly cooling the right end. The
pressure of the gas at all points in the gas-holder is
of course uniform, but greater than before any heat was
applied, just as the potential of all parts of A in 4 is
uniform, but greater than in 1. The quantity of gas
in the gas-holder, like the quantity of electricity in A,
remains unaltered, whereas the density or weight of a
cubic inch of the gas at the cold end is greater than
124 PRACTICAL ELECTRICIT-S. [Chap. III.
before, while the density at the hot end is less than
before, just as the density at the right side of a is greater,
and at the left side less than in 1.
8. Next let p, an insulated uncharged conductor, be
brought near m, a negatively charged body, then the
"^ I potential of p is negative, since negative electricity would
^ ^ go from it to the ground if it were put to earth by a
conducting wire; the density on the side next m is
positive, and on the side away from m is negative, and
Fig. 46.
the charge on p is nought, since no electricity has been
put into it or taken away from it.
9. Without moving p or m, let p be connected with
the earth, then its potential is nought, the density on the
side next m is positive and greater than before, nought on
the side away from m, and the charge on p is positive,
+ Q, say.
10. Now let the wire connecting p with the ground be
removed, and let p and m be separated slightly, then the
potential of p is positive ; the density on the side next m
is positive, but not so great as it was before p and m were
separated ; on the side of p away from m there is a slight
positive density, and the charge on p remains -}- q.
Chap. III.] POTENTIAL DIFFERENCE GALVANOMETERS. 125
11. Let M be brought nearer p than in 9, then the
potential of p becomes negative, because negative elec-
tricity will go out of p if it be put to earth ; the density
on the side next m will be positive, and greater than
in 5>, while the density on the side away from m will be
slightly negative, and the charge, as before, -f Q.
p is therefore in such a condition that its potential
will be nought without being connected with the ground
if M be brought to the same distance from p that it was
in 9 ; its potential will be positive if m is farther away, as
in 10, and negative if m is nearer, as in 11.
All this can be very well seen experimentally if M
(Fig. 42) be charged negatively, and p be connected with
the tin-foil coating of the electroscope for a moment and
then insulated when m is at a certain distance d from p,
and parallel to p. Then, when m is at a greater distance
than d from p, the gold-leaves will diverge with positive
electricity, or the potential of p is positive ; whereas if M
be at a less distance than d from p, the gold-leaves will
diverge with negative electricity, or the potential of P is
negative ; and when m is at a distance d from p, the gold-
leaves will not diverge at all, or the potential of p is
nought. In the above, m is supposed to be moved parallel
to itself, and along a line perpendicular to p, otherwise
the distance from p will not accurately determine its
position relatively to that of p.
70. Static and Current Methods of Measuring
Potential Differences Compared. — To measure the
pressure of steam or of water, a static pressure gauge
is a very convenient and sensitive instrument ; whereas,
on account of the extreme smallness of the forces
produced by the attractions of ordinary charges of
electricity, a static method of measuring a small electric
potential is either most insensitive, or requires the
employment of a delicate piece of apparatus that can
only well be used in a laboratory, hence such a measure-
ment cannot at present be performed with any portable
apparatus. In fact, a static portable electrometer, that
126 PRACTICAL ELECTRICITY. [Chap. III.
will measure accurately a small fraction of a volt, is at
present a great desideratum.
But just as the pressure of water at any given point
in the side of a vessel containing it can be ascertained
by measuring the flow of water that is produced through
a particular pipe inserted in an opening in the side
of the vessel at the point in question, so the potential
difference between two bodies can be ascertained
by measuring the current that is produced through
a particular wire used to electrically connect these
two bodies; for it can be shown experimentally (see
§ 75, page 135) that if the current passing through
a particular wire be measured in amperes, and the
potential difference maintained at the ends of the wire
be measured in volts, by means of, say, a quadrant
electrometer, the number of amperes is directly pro-
portioned to the number of volts. In the case of water
this current method would be most troublesome to carry
out practically, on account of the alteration of flow
produced by bends and irregularities in the sectional area
of the pipe, and especially because slight changes in the
mode in which the water enters the pipe, arising from
slight differences in the way in which the pipe is
attached to the vessel, produce decided changes in the
current. But in the case of electricity this current
method of measuring potential difference is most
convenient, since for a given potential difference the
current flowing through a wire depends only on the wire
and on its temperature, and not at all on the shape the
wire is made to assume, or on the form of the coil
in which the wire is wound ; nor does the current depend
on the exact way in which the ends of the wire are
joined to the two bodies, provided only that the contact
at each end is a clean metallic one. A galvanometer^
then, which directly measures current may be used to
indirectly measure potential difference.
Both in the case of measuring water-pressure and
electric potential, the production of a current through
Chap. nX] POTENTIAL DIFFERENCE GALVANOMETERS. 127
the test-pipe or wire tends to diminish the very thing we
desire to measure. Hence, unless there be some efficient
means of keeping up the water-pressure, or the electric
potential difference, we must be content to employ only
a small current, and use a proportionately delicate in-
strument to measure it. In some cases — as, for example,
with two insulated ordinary metallic bodies charged
to a different electric potential — the current method of
measuring this potential difference would be practically
impossible, as the potential difference which it was our
object to measure would, by joining the bodies together
with the wire of a galvanometer, be entirely neutralised
before the needle of the most delicate galvanometer
beeran to move. In such a case the static method is the
o
only one that can be employed.
71. When a Potential Difference Galvanometer
may be Employed. — In all cases, however, where there
exists some means of keeping the potential difference
constant between two bodies even after they are allowed
to discharge one into the other through the coil of a
galvanometer, this galvanometric method of measuring
potential difference can be employed. If the coil of the
galvanometer is made of a long fine wire, there is much
less chance of the potential difference being altered by
the application of the galvanometer than if it were made
of a short thick wii-e, and for that reason potential
difference galvanometers are wound with a long fine wire.
In certain special cases, before the application of our
galvanometers, the two bodies whose potential difference
we desire to measure are already joined by a short thick
wire — as, for example, two parts near together in a
circuit carrying a current — and in such cases the wire
used for the coil of the galvanometer employed to
measure the potential difference between these two
points need not be very long or fine. Generally, how-
ever, a long fina wire must be used in making a potential
difference galvanometer.
For practical purposes a potential difference galvano-
128 PRACTICAL ELECTRICITY. [Chap. ni.
meter must, like an ammeter, be calibrated absolutely ;
only in this case it is not the number of amperes, or
fraction of an ampere, passing through the instrument,
and producing any particular deflection, that we desire
to know, but the number of volts that must be main-
tained at the terminals of the instrument to produce this
current.
72. Voltmeter. — The permanent magnet proportional
galvanometer described in § 37, page 76, may be wound
with fine wire instead of with thick, and calibrated in
volts by ascertaining, by means of a standard electrometer,
for example, the number of volts necessary to be main-
tained at its terminals to produce various deflections of
its needle ; such a dead-beat potential galvanometer when
direct-reading is called a ^^ voltmeter,^' and it may be
taken temporarily as our commercial instrument for
measuring potential differences.
Other and more modern forms of potential difference
galvanometers are described in Chapter VIII., and the
advantages and disadvantages of some of the various
types entered into. Methods of practically calibrating
voltmeters are also given in § 213, page 408, to § 215.
129
CHAPTER IV.
RESISTANCE AND ITS MEASUREMEl^f.
73. Resistance— 74. Ohm's Law — 75. Experimental Proof of Ohm's
Law — 76. Comparing Resistances — 77. Simple Sabititution
Method of Comparing Resistances — 78. Plug Key — 79. Potential
Difference Method of Comparing Resistances — 80. Ohm — 81. Volt,
Practical Definition of — 82. British Association Unit of Resis-
tance— 83. Variation of Resistance with Length — 84. Construction
of Coils ; Multiples of the Ohm — 85. Variation of Resistance with
Sectional Area — 86. Variation of Resistance with the Material — 87.
Variation of Resistance with Temperature — 88. Construction of
a Differential Galvanometer — 89. Construction of Plug Resistance
Boxes — 90. Law of the Variation of Resistance with Temperature
— 91. Resistance of Metals per Cubic Centimetre and per Cubic
Inch — 92. Resistance of Metals for a given Length and Diameter,
or for a given Length and Weight — 93. Comparison of Electric
and Heat Conductivities — 94. Material Used in Resistance Coils —
95. Mode of Winding Resistance Coils — 96. Calibrating a Galvano-
meter by Using Known Resistances — 97. Wheatstone's Bridge — 98.
Superiority of tlie Wheatstone Bridge over the Differential Gal-
vanometer, and conditions affecting the Sensibility of the Bridge
— 99. Commercial Form of Wheatstone's Bridge — 100. Bridge
Key — 101. Use of a Shunt with the Bridge— 102. Meaning of the
Deflection on a Bridge Galvanometer — 103. Shunts — 104. Multi-
plying Power of a Shunt — 105. Combined Resistance — 106. Con-
struction of a Shunt Box — 107. Increase of the Total Current
produced by the Employment of a Shunt. — The Use of Shunts with
a Differential Galvanometer — 108. Sliding Resistance Boxes— 109.
Measuring a Resistance during the Passage of a Strong Current
—110. Ohmmeter — 111. Amoimt of Heat generated by an Elec-
tric Current — 112. Cooling Correction of the Observed Rise of
Temperature Curve — 113. Measuring a Current by the Rate of
Production of Heat — 114. Work done in an Electric Circuit — 115.
Work done by a Current Generator. Electromotive Force — 116.
Variation of External Resistance, Current, and Potential Differ-
ence at the Battery Terminals.
73. Resistance. — Whenever an electric current is
passing through a circuit, a certain amount of obstruction,
or ^^ resistance, ^^ is offered to the current, and we have
seen that, by the insertion of a longer or shorter piece of
wire, or of a longer or shorter column of liquid into a
circuit, the current can be diminished or increased in
strength. Any number of amperes can he sent through
i
130 PRACTICAL ELECTRICITY. [Chap. IV
any body, provided that we Jmve a sufficiently powerful
generator, and provided that the body is not fused or
otherwise destroyed by tlm current before the current has
reached the required strength. Hence, we cannot
measure the magnitude of the electric resistance of a
body by the smallness of the current strength unless we
know something about the power of the generator, just
as the number of gallons of water per minute passing
through a pipe furnishes no indication of the resistance of
the pipe unless we know the difference of pressure main-
tained at the two ends which is driving the water
through the pipe. If, however, the same electric potential
difference be maintained at the ends of one wire A as
is maintained at the ends of another b, then the resistances
of these wires will be inversely proportioned to the number
of amperes flowing through them respectively ; or more
generally, the resistance is proportional to the ratio of
the potential difference maintained at the ends of the wire
to the strength of the current flowing through it,
74. Ohm's Law. — Experiments originally made by
Ohm in 1827, and verified to a high degree of accuracy
by an elaborate series of experiments made at the
Cavendish Laboratory at Cambridge some years ago, show
that this ratio of potential difference to current is abso-
lutely constant for a definite piece of m^etal at a constant
temperature, and may be called simply the " resistance "
of that piece of metal.
76. Experimental Proof of Ohm's Law. — To test
Ohm's law it is necessary to employ a more delicate
statical potential difference measurer than a gold leaf
electroscope, and a form of Sir W. Thomson's quadrant
electrometer, constructed by Dr. Edelmann, of Munich,
and shown in the following figures, may be con-
veniently employed for this purpose. The instrument
rests on a metallic bracket l (Figs. 47, 48), screwed
to the wall, and is levelled by means of the three
levelling screws, g g (Figs. 47 and 48) are four quar-
ters of a brass cylinder insulated from one another,
Chap. IV.]
QUADRANT ELECTROMETER.
131
and held in position by ebonite collars R r and s s
(Fig. 48). These quarter cylinders are connected together
Fig. 47.
in opposite pairs by means of two pieces of wire, the
first and third being also attached to the "electrode ""^ A
(Fig. 47), and the second and fourth to the electrode b.
* ^' Electrode ^^ is the name given to a wire or rod by means of
which a current enters or leaves a piece of apparatus.
132
PRACTICAL ELECTRICITY.
[Chap. IV.
Suspended inside this system of quarter cylinders, there
hangs, by means of a fibre of unspun silk, a movable
rig. 48.
piece of aluminium w w, shaped as shown in elevation in
Fig. 48, in plan in Fig. 49, and in perspective in Fig. 50,
and which may be called the needle. This movable
Chap. IV.] QUADRANT ELECTROMETER. 133
arrangement, or needle, has attached to its bottom a
looped platinum wire, to which is fastened a small piece
of sheet platinum, p (Figs. 47, 48, and 50), dipping into
a small quantity of sulphuric acid, contained in the
glass vessel t, and electrically connected with the
wire p by means of the platinum wire r, which dips
into the acid. Into a small collar q (Fig. 50), at the
top of this needle, there is fixed a little stem of tortoise-
shell, carrying the mirror s, which reflects a ray of
light through the window f (Figs. 47 and 48), on to a
distant scale, in accordance with Sir W. Th'^mson's re-
flecting arrangement already described
in § 54, page 103.
The movable arrangement w w is
kept at a high potential by one end
of what is called a " dry pile " (see
§ 197, page 372) being attached to the
wire p, which passes through a collar
E, let into the outer glass vessel z, the
other end of the dry pile being attached
to the brass framework d d of the instrument. When all
the four quarter cylinders are brought to the same potential
by connecting the electrodes a and b together with a piece
of wire, then no matter how highly the needle be charged,
it will, except for the extremely small torsion produced
by the silk fibre, which can be made insignificant by
turning round the head f, rest in any position if turned
round a vertical axis passing through its centre. But
when all the four quarter cylinders are at the same poten-
tial, we want the spot of light to stand at nought on
the scale, hence it is necessary to give directive force
to the needle ; this is done by means of a small magnet
ns fastened to it, as seen in Figs, 48 and 50,. and
a controlling magnet which turns the needle so that
it rests in the symmetrical position shown in Fig. 49,
when all the four quarter cylinders are at one potential.
The deflection of the needle, or the motion of the spot of
light on the scale, which is proportional to this deflection,
134
PRACTICAL ELECTRICITY.
[Chap. IV.
is very nearly directly proportional to the difference of
potential between the opposite pairs of quarter cylinders
as long as the potential difference between the needle
w w and the outside of the instrument is constant, and
the magnetic controlling force produced by
the outside controlling magnet is unaltered
in magnitude or direction.
The complete formula for a given position
of the controlling magnet may be proved to
be as follows : — Let N be the potential
difference between the needle and the
framework of the instrument, P the poten-
tial of one pair of quarter cylinders rela-
tively to the framework d, and Q the
potential of ' the opposite pair of quarter
cylinders also relatively to the framework,
d the deflection of the spot of light on the
scale from the zero position, then
^cx:(P-Q){N-J(P + Q)},
from which it follows, first, that the sensi-
the instrument increases as N increases;
that d becomes more and more nearly pro-
portional to P — Q as N becomes larger and larger.
This formula is calculated on the supposition that the vertical
edges of the needle w are never very near the vertical edges of the
stationary quarter cylinders. With such a short needle as is shown in
the figure, and which correctly illustrates the apparatus as made by
Dr. Edelmann, this condition is far from being fulfilled when the
needle is deflected. Hence the instrument would be improved if each
half of the needle were made broader, even though the moment of in-
ertia would thereby be increased, the consideration which has probably
influenced Dr. Edelmann in making it so narrow. Another improve-
ment would consist in supporting the glass vessel T from ebonite rods
instead of by the ebonite ring s s, since leakage takes place from the
sulphuric acid in the vessel, over the surface of the ebonite ring s s,
to the quarter cylinders G, G, and, consequently, if either pair be left
entirely insulated, even for a short time, the spot of light rapidly
moves off the scale, from the potential of this insulated pair of quarter
cylinders being raised by the electricity leaking into them.
Fig. 51 shows diagrammatically the quarter cylinders
cc, c'c' of the Edelmann electrometer joined to the
bility of
secondly.
Chap. IV.]
PROOF OF OHM'S LAW.
135
terminals T, t' of a resistance R through which a current is
sent by the battery b, and its strength measured by the
111 M^
galvanometer g. As the wire r is long and rather fine,
in order that the potential difference at its terminals may
be large enough to be measured with the electrometer, it
136 PRACTICAL ELECTRICITY. [Chap. IV.
would be necessary, if we wished to vary the current
considerably, by iucreasing the resistance in circuit, to
introduce a resistance in the circuit several times as
great as the resistance offered by the wire r. A simpler
plan than employing such large resistances consists
in varying the number of cells used to send the current,
and this is easily done by keeping one wire attached
to the binding screw Sq and attaching the other wire to
the screw s^ or Sg, &c., according as we wish the current to
be sent by one or two, &c. cells. If the current be varied it
will be found that if simultaneous readings of the electro-
meter and galvanometer are taken for the different currents
that the ratio of potential difference to current is constant.
76. Comparing Resistances. — The simplest way
of insuring that the same potential difference — that iS',
the same number of volts — shall be maintained at the
ends of two wires is to join the wires in parallel
circuit, as shown in Fig. 62, or what may be called
simply "m parallel." The number of amperes flowing
in the two circuits can be measured, of course, by pro-
perly calibrated galvanometers put in the two circuits,
but the coils of each of these galvanometers must be made
of such a short piece of thick wire that the insertion of
the galvanometer in either of the circuits does not
weaken the current in that circuit, otherwise the
number of amperes will not be inversely proportional
simply to the resistances of the wires a and b, but to the
resistances of the two circuits, increased by the addition
of the resistances of the respective galvanometers.
It may here be noticed that a properly calibrated
galvanometer always measures the current flowing
through the circuit in which it has been placed. But it
does not, of course, follow that the current is the same
as it was before the insertion of the galvanometer, there-
fore if it is the latter we desire to measure care must be
taken that the insertion of the galvanometer shall not
diminish the current. Just in the same way when
measuring temperature, a thermometer put into a vessel
Chap. IV.] COMPARISON OF RESISTANCES. 137
of liquid always measures quite accurately the joint
temperature of the liquid and thermometer ; but except
in the very exceptional case of the thermometer bulb
and the liquid being at the same temperature before the
insertion of the thermometer bulb (so that the mercury
neither rises nor falls when the thermometer is inserted),
the thermometer will either slightly raise or slightly
lower the previous temperature of the liquid, unless the
volume of the bulb be very small compared with the
volume of the liquid, or, more accurately, unless the
thermal capacity of the bulb and liquid in it is very
small compared with that of the liquid and vessel
combined into which it is placed. And for that
reason, thermometers with extremely small bulbs, contain-
ing very little mercury, have frequently to be employed.
So a current galvanometer should have as small a
resistance as possible, and, for a similar reason, as we
have already seen, a potential difference galvanometer
should have as high a resistance as possible, so as to fulfil
the general law which must be carefully attended to in
all experiments — the test must not alter the thing tested.
By comparing, then, the currents sent through two
wires, at the ends of which the same potential difference
is maintained, their resistances can be compared, and in
this way two resistances can be made, for example, equal
to one another. But as the insertion of the galvano-
meter will generally increase the resistance of the circuit
in which it is placed, two galvanometers of known
138 PRACTICAL ELECTRICITY. [Chap. IV
resistances and with known absolute calibration curves
should be employed.
77. Simple Substitution Method of Comparing
Resistances. — The following ^'■simple substitution method"
is, however, much simpler to be used when one resistance
has to be made equal to another, as it requires the
employment of only one galvanometer of unknown
resistance, and of which even the relative calibra-
tion need not be known, much less its absolute
calibration ; in fact, a simple galvanoscope, that merely
indicates more or less as regards the current, is all
that is needed. Put any convenient electric generator
in circuit with a galvanoscope and a wire whose re-
sistance we wish to reproduce, and observe the deflection.
Next remove this wire, and put in its place another
wire, with which a smaller deflection is obtained, on the
same galvanoscope using the same generator. Now
gradually diminish the length of the second wire until the
original deflection is reproduced, then the resistance of the
new wire will be exactly equal to that of the old. In mak-
ing the experiment, it is desirable to select for the second
wire one which, as already stated, gives a smaller deflec-
tion, and therefore has a larger resistance than the first,
so that by shortening it its resistance may be made equal
to the first. We shall see, however, later on, that even if
the deflection with the second wire be too large instead
of too small, so that it has too small and not too large a
resistance, the resistance of the second may be increased
and made equal to that of the first wire by passing it
through a draw-plate, so that it becomes thinner and of
smaller diameter. But this is not nearly so easy an adjust-
ment as shortening a wire that has been selected with too
great a length.
To detect any possible change in the sensibility of
the galvanoscope, or in the power of the generator during
the test — a change in either of which would, of course,
destroy the accuracy of the test — it is well after the second
wire has been altered, until the first deflection on the
Chap. IV.] SIMPLE SUBSTITUTION METHOD. 139
galvanoscope has been nearly reproduced, to substitute the
lirst wire for the second, and see whether the deflection
now obtained with the first wire in circuit is exactly the
same as was originally obtained. If it be found to be
slightly different, then the final adjustment of the second
wire must, of course, be made with the new deflection
of the galvanometer obtained with the first wire in
circuit, and not with the deflection that was origin-
ally obtained when the first wire was in circuit. While
making the preceding test, care must be taken not to
alter the sensibility of the galvanometer by accidentally
Enmn
Fig. 53.
moving the controlling magnet, and it is well not to keep
the current flowing continuously for too long a time, as
the battery is liable to become what is called "po?amec?,"
and the current in consequence diminished.
The preceding method of comparing the equality of
two resistances is exactly analogous with what is known
as Borda's method of double weighing, by means of
which the true weight of a body can be accurately deter-
mmed, no matter how unequal be the lengths of the
two portions of the beam, or how unequal the weights
of the pans of the balance employed.
78. Plug Key. — In order to connect the galvanoscope
and current generator quickly and conveniently with
either the known or the unknown resistance, the plug key,
shown in Fig. 53, may be employed. It consists of three
pieces of brass A, b, and c fastened to a slab of ebonite
140 PRACTICAL ELECTRICITY. [Chap. TV.
or wood E E. B J inserting the conical brass plug P into the
hole H, the current produced by the battery, one end of
which is attached to b, will pass through the unknown re-
sistance, whereas if it be inserted in h it will pass through
the known resistance and not through the unknown.
79. Potential Difference Method of Comparing
Resistances. — Another method of comparing two resist-
ances, depending directly on the definition of resistance,
consists in sending a current through the two wires a b and
CD placed " in series,''^ or end on (Fig. 54), and comparing,
by means of a suitable galvanometer, the potential dif-
ference between a and b with that between c and d.
For since the same current passes through these two
Fig. 5i.
wires, and since resistance is the ratio of potential
difference to current, it follows that —
resistance of AB potential difference between A and B
resistance of CD~ potential difference between C and D
80. Ohm. — The legal unit of resistance, as settled
by the International Electrical Congress, at their meet-
ing held in Paris in 1884, is that of a column of pure
mercury 106 centimetres long, 1 square millimetre in
sectional area, at a temperature of 0° C. This is called
the " ohm,'^ and is the only one of the electrical units
that has yet been legalised. All the others have, how-
ever, been accurately defined in terms of the ohm and
the ampere, but as the exact rate of chemical action
corresponding with the ampere (although now generally
accepted as being that given in § 6, page 11) has not
yet been defined legally, it cannot be said that a practical
unit of current has yet been legally adopted, and the
same remark applies to the volt and to all the electrical
units depending on the ampere.
Chap. IV.-j THE OHM, THE VOLT, THE B. A. UNIT. 141
81. Volt, Practical Definition of. — A volt is the
difference of potentials that must be maintained at the
ends of a wire of one ohm resistance, so that a current
of one ampere may pass through it ; or generally, if Y
be the potential difference in volts maintained at the end
of a conductor having a resistance of o ohms, and if
A be the current in amperes flowing through it
o
82. British Association Unit of Resistance. — Pre-
vious to 1884, the unit of resistance used most exten-
sively in Great Britain and elsewhere was the British
Association^ or "^. A." unit, called also previously to
1884 an ohm. The name ohm is, however, now restricted
to the legal unit, and the older one is called a B. A. unit.
The value of this latter was decided on by the Electrical
Committee of the British Association, after years of
extremely careful and painstaking work, and copies of
the standard were first issued in 1865, since which time
they have been multiplied almost indefinitely. The ideal
B. A. unit (as distinguished from the actual one, which,
as will be explained farther on, is slightly wrong) is a
derived unit, and not an arbitrary one, that is to say, it is
selected so that the equations connecting current, resist-
ance, potential difference, work, &c., shall be of the
simplest kind, without arbitrary co-efiScients. The great
value of this so-called absolute, or British Association,
system of electrical units was fully accepted at the meet-
ing of the International Electrical Congress at Paris in
1881, and it was decided that for purposes of reference,
that particular length of a column of mercury one milli-
metre square in section which at a temperature 0"^ Centi-
grade was found to have most nearly the true B. A. unit
of resistance, should be called the ohm, and legalised.
Doubts having arisen as early as 1878 as to whether
there had not been some mistake made by the British
Association Committee in their original determination,
142 PRACTICAL ELECTRICITY. [Chap. IV.
the whole work was repeated, and it was eventually
agreed, at the meeting of the Conference in 1884, that
the length of mercury which, having one square milli-
metre in section, had at 0° 0. one ohm resistance should
be internationally accepted as 106 centimetres, the deci-
mal of a centimetre which required to be added to make
this length perfectly accurate being left for further
experiment and consideration. And in England it has
been also decided that for the purposes of issuing practical
standards of electrical resistance, the number of B. A.
units adopted, from the means of a large number of
experiments, as the resistance of a column of mercury
100 centimetres 1 square millimetre, at 0° Centigrade,
which is the ^^ Siemens' unit of resistances^' shall be
0-9540.
Therefore it follows that
1 legal ohm = 1'0112 B. A. units.
1 B. A. unit = 0-9889 legal ohm.
Example 21. — With a potential difference of 108
volts maintained at the terminals of an Edison incande-
scent lamp, 0-75 ampere passes through it, what is the
lamp resistance? Answer. — 144 ohms.
Example 22. — If the potential difference be reduced
to 105 volts, and the resistance of the lamp remain the
same, what current will now pass through it %
Answer. — 0-729 ampere.
Example 23. — If a wire have 127-4 B. A. units' resist-
ance, what is its resistance in legal ohms 1
Answer. — 126*0 ohms.
Example 24. — If a wire of uniform section have 27
B. A. units' resistance, how much per cent, must be cut off
it so that it may have 26 ohms' resistance ?
27 B. A. units = 27 X 0-9889 ohm.
Answer. — 26*7 ohms.
Chap. IV.] VARIATION OF RESISTANCE WITH LENGTH. 143
Answer. — To reduce to the 26 ohms we must cut off
^1^, or about 2*6 per cent.
Examiyle 25. — What percentage error would be made
in assuming that the B. A. unit was the same as the
legal ohm?
Answer. — The resistance would be assumed to be
about 1 '1 per cent, larger than it really was.
To familiarise the student with the practical value of
an ohm, it may be mentioned that a copper wire one foot
long, Y^oo^^^^ ^^ ^^^ i^^^ i^ diameter, has roughly 10 ohms'
resistance, which is also roughly the resistance possessed by
a mile of iron wire one-Hfth of an inch in diameter.
83. Variation of Resistance with Length. — The
apparatus shown in Fig. 55 is adapted for ascertaining
this, and consists of a thin platinum wire of uniform
sectional area, stretched along the graduated bar between
the two points w, w', and through which, on pressing down
the key, a constant current flows, produced by some cur-
rent generator attached to the two wires which come
from the binding screws at the farther side of the figure.
144
PRACTICAL ELECTRICITY.
[Chap. IV.
To one end w is joined one terminal b of a tangent
galvanometer, the coil of which is wound with a very fine
wire, and to the other terminal b' is attached a flexible
wire, by which it can be electrically attached to any
other point of the stretched platinum wire by means of
the binding screw s'. Experiment shows, that if the
sensibility of the tangent galvanometer is kept unchanged
by the adjusting magnet m not being moved, the tangent
^^m^m^^
Fig. 56.
of the deflection is directly proportional to the distance
w s'. Now, the resistance of the wire forming the coil of
the tangent galvanometer is very great compared with
that of the stretched platinum wire w w', hence it follows
(see § 71, page 127) that the potential difference between
the points w and s of the stretched wire is unaffected by
the presence of the galvanometer. Consequently we may
conclude that the tangent of the deflection measures the
potential difference that would exist between the points w
and s' if the galvanometer were not present. Hence,
when a constant current is flowing through a particular
Chap, IV.] CONSTRUCTION OF RESISTANCE COILS.
145
wire, the potential difference between two points is
directly proportional to the length of wire between those
two points, so that potential difference divided by cur-
rent which we have defined as the measure of resistance,
is directly proportional to the length of wire.
This experiment can be performed for greater lengths
of wire by replacing the stretched wire shown in the
last figure by lengths of the same wire wound for con-
venience round in a screw groove turned on a wooden
cylinder. Fig. 56 shows such an arrangement, consisting
of six coils of iron wire of lengths, say 5, 10, 20, 30, 40,
and 50 feet respectively, all the wire being drawn to
have exactly the same diameter, say 0-0095 inch.
From what has preceded it follows that, if distances
OA, OB, &c. (Fig. 57) measured horizontally from a point
o, represent the resistance of a circuit from some fixed
point up to various points of the circuit, and if vertical
distances op, a q, &c., represent the potentials at these
points, the points P, Q, R, s, Sfc, will lie in one straight
line when the current is steady, and the tangent of the
angle this line makes with o c will measure the strength
of the current, this strength being in amperes if the re-
sistances are measured in ohms, and the potentials in
volts.
84. Construction of Coils; Multiples of the Ohm.
— We are now in a position, if we have a single wire
having one ohm resistance to start with, to construct, in
the following way, by the simple substitution method, coils
having a resistance of any number of ohms we please.
First, make a second coil having one ohm resistance, then
K
146 PRACTICAL ELECTRICITY. fChap. IV,
put these two ohm coils in series as in Fig. 54, page 140,
when the resistance of the two will be, as we have seen,
two ohms. Now make a single coil, having two ohms'
resistance by comparison, then using this in series with
one of the one- ohm coils, we shall have a resistance equal
to three ohms, compared with which we can then make
a single coil having three ohms' resistance, and so on,
85. Variation of Resistance with Sectional Area.
— For the purpose of testing experimentally how the
resistance of a wire depends on its sectional area, which
may be done by the simple substitution method, a board
somewhat like that shown in Fig. 56 is employed, but
having wires of exactly the same length (say twenty-one
feet) and the same material (iron) wound round each of the
cylinders. The sectional areas of these wires are how-
ever different, being proportional to the squares of the
diameters, which may be 0-0195, 0*0158, 0-0136, 0-0106,
0-009, 0-0078 of an inch.
86. Variation of Resistance with the Material. —
On the cylinders of a third board are wound wires of
exactly the same length (say twenty-one feet), and drawn
to have exactly the same diameter (say 0-012 of an inch),
but made of the following materials : copper, platinum,
brass, iron, lead, and German silver, from which the effect
of difference of material can be ascertained.
As in selecting a piece of wire there are three
distinct things that have to be considered — its length,
its thickness, and the material of which it is made —
it is important that the change in the resistance pro-
duced by a change in each of these three things
should be separately measured ; and generally, in experi-
menting, when it is possible to change several of the con-
ditions under which the experiment is made^ it is of the
utmost importance that only one of the conditiorvs shoidd
he varied at one time. The effect produced by the varia-
tion of one condition should be fully inquired into before
any one of the other conditions is in any way altered,
otherwise it will be generally quite impossible after-
Chap. IV.] TEMPERATURE VARIATION OF RESISTANCE. 147
wards to gather from the results what portion of the
variation in the effect is produced by any particular
change in the conditions.
87. Variation of Resistance with Temperature. —
We have already said that the resistance of a wire
Fig. 58
depends on its temperature, and the apparatus shown in
Fig. 58 is arranged especially for testing this. A coil
of silk-covered iron wire is wound on a long, thin, hollow
wooden bobbin, the top of which is seen at A. This bobbin
is placed in a long thin glass tube, which itself is placed
in water contained in the vessel v, the temperature of
which can be raised by the Bunsen gas-burner b. s is
the top of a piece of stout brass wire attached to a flat
148 PRACTICAL ELECTRICITY. LChap. IV.
piece of wood in the vessel v, and by means of which
the water can be stirred up and its temperature made
fairly uniform throughout. The temperature of the coil
of wire is shown by the thermometer t, the bulb of which
is inside the thin hollow wooden bobbin ; but as even
with this arrangement there may be a difference of tem-
perature between the wire and the thermometer bulb,
if the heating of the water is performed rapidly, it is
better, before making a measurement of the resistance
in the manner about to be described, to withdraw the
Bunsen lamp, and wait a few minutes for the interior of
the water-bath all to settle down to a uniform tempera-
ture, which is indicated by the two thermometers t
inside the wooden bobbin, and t' in the water-bath out-
side the bobbin indicating the same temperature. The
double screen D D is for the purpose of preventing the heat
radiated from the lamp warming the apparatus used for
measuring the resistance, the action of which is based
on the mode of measuring resistance shown in Fig. 52,
page 137. From what was there said, it follows that if
the currents flowing through A and b are equal, then the
resistances of A and b are also equal. This equality of the
currents might be ascertained from the deflections of two
galvanometers placed in the circuits a and b, these
deflections not being necessarily equal, but having values
which the absolute calibration curves of the galvano-
meters show to correspond with equal currents.
This test could, however, more easily be made if, instead
of using two separate galvanometers, a galvanometer were
employed containing two distinct coils c, c' (Fig. 59), one
placed in the circuit A, and the other in the circuit b,
and if the positions of these coils relatively to a sus-
pended magnetic needle were so adjusted, that on equal
currents passing through them their effects on this
needle exactly balanced one another, so that the resultant
deflection of the needle was nought. With such an ar-
rangement a deflection nought of the needle would indicate
that the resistances of the complete circuit A, including
Chap. IV.] DIFFERENTIAL GALVANOMETER. 149
that of the coil c, was equal to the resistance of b, in-
cluding that of the coil c'. Further, if these coils not
only had equal and opposite effects on the needle when
equal currents were passing through them, but had also
equal resistances, then a deflection nought of the needle
would indicate not merely that the resistances of the cir-
cuits A and B, but also that the resistances of the re-
mainders of the two circuits a and b, after excluding the
resistances of the two coils c and c', were also equal.
Hence, with the conditions of equal magnetic effect
and equal
resistance of
the two coils
c and c', it
follows that
when there _
is no deflec- Fig. 59^
tion of the
galvanometer needle, the two wires, a and b, short or long,
used to join the point p with the ends of the coils, have
equal resistances.
The instrument for measuring resistance, constructed
on this principle, is called a " differential galvanometer^^
and such a galvanometer is seen to the left of Fig. 58.
In the apparatus shown in Fig. 58, these two wires,
a and b of Fig. 59, are our experimental coil of iron wire
in the water-bath, and the wire in the resistance box r,
hence, as the resistance of the wire in the water-bath
varies by being warmed, we can, by varying the resistance
in R so as to always obtain no deflection of the needle of
the difierential galvanometer, measure the change of re-
sistance produced by the variation of temperature.
88. Construction of a Differential Galvanometer. —
The actual way in which the two conditions, equality of
7nagnetiG effects, and equality of resistance of the wires
of the two coils of the difierential galvanometer
are fulfilled, is as follows : — Two reels of silk-covered
copper wire are chosen, so that the diameter of the
150 PRACTICAL ELECTRICITY. [Chap, IV
wire on each is as nearly as possible the same, and
the two wires are wound side by side on the galva-
nometer bobbin until it is nearly full; the wires are
then tested and cut, so that the resistance, but not of
course necessarily the length, of each wire is the same.
A current is now sent in opposite directions through the
two coils in series, when it will be found that, although
the wires have been wound on side by side, one of them
will have a greater magnetic effect than the other,
partly perhaps because, being a trifle thicker, it has to be
longer than the other, so as to have the same resistance,
or partly because it is, on the whole, nearer the suspended
needle than the other. To remedy this, a small portion
of the wire having the greater magnetic effect is un-
wound, and without being cut, which would of course
destroy the equality of the resistances of the two coils,
the portion so unwound is coiled up out of the way in
the base of the instrument. In this way, by unwinding
more or less from the coil that was magnetically the more
powerful, a very good balance can be obtained. In the
use of differential galvanometers in which the needle is
suspended by a silk fibre (as, for example, it is in
Fig. 58, where the silk fibre is inside the tube <), a final
and most delicate adjustment can be obtained by raising
or lowering one of the levelling screws s s slightly, so as
to tilt the needle nearer to or farther from one of the
coils. And the spirit-level l should then be permanently
adjusted so that the bubble is in the centre of the glass
cover of the level, after the instrument has been tilted
in the manner just described. The plugs P^, P^, seen
in the figure, are for the purpose of enabling the two
coils of this differential galvanometer, which is known
as Latimer Clark's differential galvanometer, to be joined
so as to oppose one another's effect, or to assist one
another when it is desired to use the instrument as an
ordinary galvanometer instead of a differential one, and
the plugs p\ p^ are for the purpose of shunting either coil
of the differential galvanometer (see § 107, page 185).
Cliap. IV.] PLUG RESISTANCE BOXES. 151
89. Construction of Plug Resistance Boxes. — The
general construction of a resistance box was explained in
§ 12, page 28 ; but in the one shown in Fig. 58, the coils
used to connect the various pieces of brass on the top of
the box are not equal, but may conveniently have the
following values going round them consecutively, starting
from one of the binding screws :
0-1, 0-2, 0-2, 0-5, 1, 2, 4, 10, 20 ohms.
There is also an " infinity plug ^^^ that is, two of the pieces
of brass are not connected by a coil at all. Hence, if we
take out the first and second plugs, the rest being left in,
the resistance in the box will be O'l + 0*2 or 0-3 ohms ;
if we take out the first and fourth, replacing the second,
it will be 0*1 -f 0*5 or 0*6 ohms, &c. So that with the
coils above-mentioned, any resistance between 0*1 and 38
ohms can be obtained with the nine coils. The brass
plugs and the holes into which they fit are made conical,
and the plugs should be well ground into the holes during
manufacture. To prevent a resistance being introduced
between the plug and the two pieces of brass on each
side of it, a good contact is necessary, and to insure this,
a plug, when put into the hole, should receive a slight
screwing motion, when it will be found, with well-made
plugs, that, although there is no screw thread on the
plug, the whole resistance box can be easily lifted
up by taking hold of one plug after it has properly been
put in. Such closeness of contact it would be extremely
difiicult to secure by simply pressing down the plug,
unless a large downward pressure were employed, and a
corresponding tugging when taking it out, which would
soon wrench off the ebonite head. The ebonite heads
are usually screwed on to the tops of the brass plugs, but
to prevent the head unscrewing in use, a pin should
always be driven through the ebonite top and the head
of the brass plug after they have been fitted together.
The holes in the figure, seen in the brass pieces
themselves, are for the purpose of holding the plugs,
152 PRACTICAL ELECTRICITY. [Chap. IV.
when they are not placed between the pieces of brass to
short-circuit the intervening coil ; but the use of the
holes in the brass pieces cannot be recommended, since,
when the resistances corresponding with the holes that
are unplugged are being rapidly counted, a plug stuck
in one of the pieces of brass is liable to be mistaken for
a plug between two pieces of brass, and hence coils
which are actually in circuit are liable to be missed out
in the counting up. Further, unless the pieces of brass
are very large, the ebonite head of a plug stuck into one
of them prevents the next plug being properly inserted, or
removed, when the resistance of the next coil is to be
subtracted from or added to the resistance in circuit.
90. Law of the Variation of Resistance with
Temperature. — Experiments made with the apparatus
seen in Fig. 58, show that the resistance of copper
increases about 0*388 per cent, per 1° C, or 1 per
cent, for a rise of temperature of 2° -57 0. This increase
of resistance is not due simply to the wire becoming
longer, for if the change of resistance were due merely
to alteration of size, then, since the co-efficient of increase
of length by temperature is the same as the co-efficient
of increase of diameter, and as the resistance is directly
proportional to the length, and inversely proportional to
the square of the diameter, it follows that as far as mere
size is concerned, increase of temperature should diminish
the resistance. The fact, however, that the expansion
of a metal by heating has the effect of separating all
the particles of which the metal is composed from one
another, may have something to do with the greater
difficulty a current has in passing through a hot wire than
through a cold one. But even this rough figurative expla-
nation must be received with caution, since the resistance
of a liquid which also expands in all directions with
increase of temperature, diminishes as the temperature
rises instead of increasing as is the case with metals.
Yery careful experiments made on the increase of
resistance of metals with temperature, show that tlie
Chap. IV.l TEMPERATURE VARIATION OF RESISTANCE. 153
increase, although roughly proportional, is not absolutely
proportional to the increase of temperature, the resistance
increasing in fact more rapidly than the temperature for
all pure metals except mercury, so that the expression
connecting resistance with temperature must contain a
term, involving at least the square of the temperature.
The actual result obtained by Dr. Matthiessen for most
pure metals, excepting iron, is approximately
R=r (1 -f 0-003824 1 -f 0-00000126 t\
where r is the resistance at 0° C, and Kthe resistance at
any temperature i° C.
For mercury the formula is
R=r (1 + 0-0007485 «- 0-000000398 t^)i _
for the gold-silver alloy in Table I.,
R=r (1 + 0-0006999 t - 0-000000062 «2) ;
for German silver,
R=r (1 + 0-0004433 t + 0-000000152 t^) ;
for the platinum-silver alloy in Table I.,
R=r(l + 0-00031 0.
Carbon is an exception to the otherwise universal
law, that the resistance of elementary substances, as dis-
tinguished from compounds, increases as the temperature
rises. This fact is a reason for thinking that very
possibly carbon is really a compound body.
91. Resistance of Metals per Cubic Centimetre
and per Cubic Inch. — The following table, deduced from
Dr. Matthiessen's results, and expressed in terms of the
1884 legal standard (see § 80, page 140), gives the value at
0° C. of the resistance in microhms, or millionths of an
ohm, of a cubic centimetre and of a cubic inch, which
means the resistance from one face to the opposite face
across the cube.
164
PRACTICAL ELECTRICITY.
[Chap. IV.
TABLE No. I.
Chemically Pure Substances arranged in order of Increasing Mesistanct
for the same length and Sectional Area.
LEGAIi MICROHMS.
Name of Metal.
Eesistance in Microlims
at 0° Centigrade.
Cubic
Centi-
metre.
Cubic
inch.
Relative
Resist-
ance.
Silver, annealed
Copper, annealed
Silver, hard drawn . . . .
Copper, hard drawn ....
Gold, annealed
Gold, hard drawn ....
Aluminium, annealed . . .
Zinc, pressed
Platinum, annealed ....
Iron, annealed
Gold-silver alloy (2 oz. gold,
1 oz. silver), hard, or an-
nealed
Nickel, annealed
Tin, pressed
Lead, pressed
German silver, hard, or an-
nealed
Platinum- silver alloy (1 oz.
platinum, 2 oz. silver),
hard, or annealed . . .
Antimony, pressed ....
Mercury
Bismuth, pressed
1-504
1-598
1-634
1-634
2-058
2-094
2-912
5-626
9-057
9-716
10-87
12-47
13-21
19-63
20-93
24-39
35-50
94-32
131-2
0-5921
0-6292
0-6433
0-6433
0-8102
0-8247
1-147
2-215
3-565
3-825
4-281
4-907
5-202
7-728
8-240
9-603
13-98
37-15
51-65
1
1-063
1-086
1-086
1-369
1-393
1-935
3-741
6-022
6-460
7-228
8-285
8-784
13-05
13-92
16-21
23-60
62-73
87-23
From the preceding table we see that of the various
metals, annealed silver is the one having the leasts
and bismuth the one having the greatest, resistance for a
given length and sectional area.
The resistances of ^^ commercial" metals are always
higlier than the values given in the preceding tables and the
Chap. IV.] CONDUCTIVITY. 155
difference is often very considerable. As copper can,
however, now be easily obtained having as much as 95
per cent, of the " conductivity " of pure copper (which
means that the resistance of a wire of commercial copper
exceeds that of a wire of the same length and sectional
area made of pure copper by not more than 5 '3 per
cent.), copper of less conducting power than this should
not be bought for electrical purposes.
Conductivity is the reciprocal of resistance^ so that if
r^ and r^ be the resistances, and q and c^ the conduc-
tivities,
Erom the preceding table, the resistance of a wire of
any length and sectional area, at 0° 0., can be easily found,
by employing the formulae given.
Example 26. — To find the resistance of a wire 52
metres long, 1 square millimetre in section at 22° C,
made of pure copper, hard drawn.
Resistance required ) _1'634 52 x 100
in ohms J ~ 10^ 1
Too
X (1+ 0-003824 X 22 + 0-00000126 x 222).
Answer. — 0*9221 ohms.
Example 27. — To find the resistance of a wire 110
feet long ^th. of an inch in diameter at 46° C, made of
pure annealed platinum.
Resistance required ) 3-565 110 x 12
in ohms ) ~ 10^ ^ tt 1
4 ^ 203
X (1 + 0-003824 X 46 + 0-00000126 x 462).
Answer. — 2*825 ohms.
Example 28. — At what temperature will a wire 3J
156 PRACTICAL ELECTRICITY. [Cliap. IV.
miles long j^th of a square inch in section, made of
German silver, have a resistance of 22*23 ohms ?
«o«o 8-240 3-5x5280x12
^^■'^ = -Tor^ jT
12
x(l + 0-000443 < + 0-000000152 ^ t^).
Solving this quadratic equation for t, we find t equals
37°-5 C.
Example 29. — If the resistance of a sample of com-
mercial metal is 97-5 ohms, whereas the resistance of
the same piece of metal, if quite pure, would be 94*3 ohms
at the same temperature, what is its percentage conduc-
tivity in terms of that of the pure metal 1
The conductivity of the sample of ~) _ 1
commercial metal 1~ 97-5
The conductivity of the same if') _ 1 .
pure would )~ 94.3 '
. *. if £c be the percentage conductivity,
J__^_ _1_
97-5~ 100 ^ 94-3*
r. x= 96-72.
Answer. — 96-72 per cent, conductivity.
92. — Resistance of Metals for a given Length and
Diameter, or for a given Length and Weight. — It is
frequently convenient to know, not merely the resistance
of a cubic centimetre, or of a cubic inch, but of a wire of
a given length and diameter, or of a given length and
weight. The following numbers, giving the resistance
at 0° 0. of pure substances, are deduced from Dr. Mat-
thiessen's experiments, and are expressed in terms of the
1884 legal ohm. The substances are arranged in order
of increasing resistance for the same length and weighty
the order for increasing resistance for the same length and
sectional area being that given in Table No. I., page 154.
Chap. IVO
COMPARATIVE RESISTANCES.
157
TABLE No. II.
Chemically Fure Substances at 0® Centigrade, arranged in order of
Increasing Resistance for the same Length and Weight.
LEGAL
OHMS.
Besistance
of a wire
1 foot long,
weighing
1 grain.
Resistance
Resistance
Resistance
Name of Metals arranged
of a wire
of a wire
of a wire
in order of increasing
1 foot long,
1 metre
1 metre
resistance for the same
xsW^h of an
long.
long,
length and weight.
inch in
weighing
1 millimetre
diameter.
1 gramme.
in diameter.
Ohms.
Ohms.
Ohms.
Ohms.
Aluminium, annealed
0-1074
17-53
0-0749
0-03710
Copper, annealed . .
0-2041
9-612
0-1424
0-02034
Copper, hard drawn .
0-2083
9-831
0-1453
0-02081
Silver, annealed . .
0-2190
9-048
0-1527
0-01916
Silver, hard drawn .
0-2389
9-826
0-1662
0-02080
Zinc, pressed . . .
0-5766
33-85
0-4023
0-07163
Gold, annealed . . .
0-5785
12-38
0-4035
0-02620
Gold, liard drawn . .
0-5884
12-60
0-4104
0-02668
Iron, annealed . . .
1-085
58-45
0-7570
0-1237
Tin, pressed ....
1-380
79-47
0-9632
0-1682
Gold-silver alloy (2 oz.
gold, 1 oz. silver),
hard, or annealed .
2-364
65-37
1-650
0-1384
German silver, hard.
or Rnnealed . . .
2-622
125-91
1-830
0-2666
Platinum, annealed .
2-779
54-49
1-938
0-1153
Lead, pressed . . .
3-200
2-232
0-2498
Antimony, pressed
3-418
213-6
2-384
0-4521
Platinum-silver (1 oz.
platinum, 2 oz. sil-
ver), hard, or an-
nealed . . . . .
4-197
146-70
2-924
0-3106
Bismuth, pressed . .
18-44
789-3
12-88
1-670
Mercury
18-51
572-3
12-91
1-211
From this we see that of the metals aluminium has
the least resistance for a given length and weight, and
mercury the greatest ; whereas we saw from Table No. I,
page 1 54, that for a given length and sectional area it was
annealed silver that had the least resistance, and bismuth
the greatest.
158 PRACTICAL ELECTRICITY. [Cbap. IV.
Example 30, — What will be the weight of an iron
wire 100 yards long, having a resistance of 1 ohm at
0° C. ?
An iron wire 1 ft. long weighing 1 grain has 1 '085
ohms at 0° C, therefore an iron wire x ft. long weighing
X grs. has ic x 1 -085 ohms at 0° 0. Hence an iron wire
x^
X ft. long weighing y grs. has — x 1 "085 ohms at 0° C.
In the question x is 300, and the resistance is 1 ohm.
Therefore
?^^ 1-085 = 1;
y
.-. y= 3002 X 1-085 grs.
Answer. — 13 lbs. 15 oz.
Example 31. — What will be the length of a platinum
wire weighing 2-8 grains, and having a resistance of
0-7891 ohms at 250° C. ? Answer.— 1^ inches.
Example 32. — Which has the greater resistance, a
copper wire 20 feet long 0*015 inch in diameter, or a
platinum-silver wire 10 feet long 0*037 inch in diameter,
at 0° C. ^
The resistance of the copper wire will be to that of
20 X 9-612 . 10 X 146-7 , , .
the platinum as — is to 7^^ > ^^^ ^s this
ratio is 0-7973, it follows that the former has rather more
than three-quarters of the resistance of the latter.
Example 33. — What will be the resistance, at 95° C,
of a copper wire 20 metres long weighing 12 grammes,
and having 92 per cent, of the conductivity of pure
copper? Answer. — 7-092 ohms.
93. Comparison of Electric and Heat Conductivi-
ties.— The reciprocals of the numbers given in column
4 of Table No. I. will express the relative electric con-
ductivities of the metals for the same length and sec-
tional area. These numbers are given in column 2 of
Chap. ir.J ELECTRIC AND HEAT CONDUCTIVITIES.
159
Table No. III. On comparing these with the conductivi-
ties of the metals for heat for the same length and sec-
tional area as given in column 3 of Table No. III., and
which are the numbers obtained by Wiedemann and Franz,
we observe that the metals arrange themselves approxi-
mately, but not absolutely, in the same order for the two
conductivities.
TABLE No. III.
Relative Conduetivities per Cubic Unit.
Name of Metal.
Silver, annealed
Copper „
Gold
Platinum ...
Iron
Tin, pressed
Lead
Bismuth
As we experiment with worse and worse conductors,
we find that the electric conductivity diminishes much
more rapidly than the heat conductivity. For example,
the electric conductivity of copper is about lO^o times the
conductivity of vulcanised indiarubber, whereas the heat
conductivity of copper is only about 10* times that of
vulcanised indiarubber. Hence, while we can obtain in-
sulators for electricity, or bodies which relatively to the
metals do not practically conduct electricity at all, insula-
tors/or heat are unknown.
94. Material Used in Resistance Coils. — We see
then that it is not merely sufficient to know the length
and diameter of a wire as well as the material of which
it is made, but we must know also the temperature of the
wire if we wish to be sure about its resistance. Fixity of
length, diameter, and material, are easy enough to obtain,
but constancy of temperature it is much more difficult to
secure, partly on account of changes of temperature of
the room, and partly on account of the slight heating of
160 PRACTICAL ELECTRICITY. jChap. IV.
a coil of wire produced by a current passing through it.
Consequently, in the construction of resistance coils it is
important to use a metal of which the resistance changes
as little as possible with temperature, and which is not too
costly. To ascertain what that metal was, Dr. Matthies-
sen, in 1862 and 1863 — that is, in the early days of re-
sistance coils — made, on behalf of the Electrical Standards
Committee of the British Association, a large number
of very accurate experiments on the change of resist-
ance with temperature, and a few of his results are
contained in the following table.
TABLE No. IV.
Approximate Percentage Variation in Resistance per 1® C.
AT about 20° C.
Platinum-silver alloy (1 oz. platinum, 2 oz.
silver), hard, or annealed . . . 0-031
German silver, hard, or aimealed . . . 0'044
Gold-silver alloy (2 oz. gold, 1 oz. silver), hard,
or annealed 0-065
Mercury 0-072
Bismuth, pressed ...... 0-354
Gold, annealed )
Zinc, pressed > 0-365
•Tin, pressed )
Silver, annealed 0-377
Lead, pressed 0-387
Copper, annealed 0-388
Antimony 0-389
Iron . about 0-5
From this we see that, whereas (of the substances ex-
perimented on by Dr. Matthiessen) an alloy of platinum-
silver, hard or annealed, is the one of which the re-
sistance changes least by temperature, German silver,
which is a very much cheaper alloy, is nearly as good in
this respect. Hence, nearly all resistance coils are Tnade
of German silver, except when greater lightness and port-
ability are required, in which case the alloy of one part
of platinum and two of silver by weight is employed.
A new alloy, called " ^^^inoic?," consisting of German
Chap. IV.] MATERIAL FOR RESISTANCE COILS.
161
silver, with one or two per cent, of metallic tungsten
added, has been recently found by Mr. J. Bottomley to
have a resistance per cubic centimetre of about 34 mi-
crohms, or about 60 per cent, higher than that possessed
Fig. 60.
by German silver ; and, what is still more important, its
percentage variation of resistance per 1° C. is only about
0*021, or less than half that of German silver. We may,
therefore, expect that platinoid will supersede both Ger-
man silver and platinum-silver for resistance coils, if
162 PRACTICAL ELECTRieiTY. fChap. IV.
its resistance be found to be equally unchanged by lapse
of time.
Iron, we see, is the worst of the substances shown in
the table to be used in the construction of resistance
coils, as far as the temperature error is concerned ; but it
is not unirequently used when cheap resistance coils are
required for large currents, and when, as sometimes is
the case, great constancy of resistance is not necessary.
The resistance coil, when used as an accurate standard,
is wound inside a brass box b, shown in Fig. 60, so that
it may be inserted in a vessel of water v v, and its
temperature accurately noted by means of the thermo-
meter t. The brass box b for holding the coil is made
cylindrical inside and outside, with a large diameter and
small thickness, so as to expose as much surface as
possible to the water, in order that the coil inside may
acquire the temperature of the water as quickly as pos-
sible ; and the vessel v v containing the water may with
advantage have double sides, with an air-space between
them, as seen in the figure, to prevent transference of
heat between the water and outside space.
The tubes tt are to prevent the coils being short
circuited by water getting through the holes, by which
the rods w w attached to the ends of the resistance coil
are brought out. These tubes are made of brass, but
they are lined with tubes of ebonite to prevent electric
contact between these brass tubes and the rods w w.
Electric connection with these rods is made by dipping
their ends e e into little wooden cups containing mercury.
Example 34. — At what temperature, approximately,
would a German silver coil, which had one British Asso-
ciation unit of resistance at 16° C, have the resistance
of one legal ohm 1
1 legal ohm == 1-0112 B. A. units,
therefore the temperature must be raised sufficiently to
increase the resistance of the coil by 1*12 per cent.
Therefore, since the resistance of German silver increases!
Chap. IV.] MODE OF WINDING RESISTANCE COILS. 163
0*044 per cent, per degree, as stated in the last table, if t
be the temperature above 16° to which the coil must be
raised,
0-044 X t= M2,
or i^ = 25°'5 approximately.
Answer. — The B.A. coil will have a resistance of one
legal ohm at 41°-5 0.
Example 35. — A set of resistance coils made of plati-
num-silver are correct at 14° C. Between what limits of
temperature approximately may they be used without
correcting the results, if the temperature error is not to
exceed J per cent. ?
The resistance of platinum-silver increased about
0-031 per cent, per 1° 0., as stated in the last table;
therefore, if t be the number of degrees above or below
14° 0., within which the coils may be used without the
error exceeding \ per cent.,
0031 X t = 0-25,
. •. < = 8°.
Answer. — The limits of temperature are approxi-
mately 6° and 22° C.
Fxample 36. — If the greatest change of temperature
at some particular place between summer and winter is
from — 8° to 25° 0. in the shade, what is the greatest per-
centage variation in the resistance of a set of German
silver coils ■? Answer. — 1*45 per cent.- approximately.
Example 37. — At what temperature would a metre of
mercury one square millimetre in section have one ohm
resistance % Answer. — 8 3° -3 C.
95. Mode of Winding Resistance Coils. — Not only
must a special metal be employed in making resistance
coils, but the wire must not be wound on the bobbin in
the ordinary way. If it were wound on the bobbin as
cotton is on a reel, then each bobbin in a resistance box
would act as a magnet when a current passed through
164 PRACTICAL ELECTRICITY. fChap. IV.
it, and a box full of electro-magnets would be a most
inconvenient thing to have near a delicate galvanometer
used in testing resistances, since one would be constantly
in doubt as to whether the deflection observed on putting
on the current was due to want of adjustment in the
resistance, or to the temporary magnetisation of the
adjacent resistance box. Hence, the wire of a resistance
coil is wound back on itself as shown in Fig. 7, page 28,
8o that the current, in passing through the wire, first goes
several times round the bobbin in one direction, and
then an equal number of times in the opposite direction,
and the two magnetic effects neutralise one another.
The disturbing magnetic effect that might otherwise
have arisen when using resistance coils, is overcome by
this double mode of winding ; but the magnetic action of
a current passing round an ordinary reel of wire, or a
coil wound for a galvanometer or for an electromagnet,
&c., must be carefully taken into consideration when
anything of this form has to be tested for resistance. As
such coils are frequently wound before being tested, they
must, when it is desired to test them, be placed so far
away from the galvanometer that the mere passage of the
current round the coil produces by itself no deflection of
the galvanometer needle, when no current is allowed to
pass through the galvanometer.
96. Calibrating a Galvanometer by Using Known
Resistances. — From Ohm's law (§ 74, page 130), it follows
that the current passing through any circuit is inversely
proportional to its resistance if a constant potential
difference be maintained at the ends of the circuit. Con-
sequently if a constant potential difference be maintained
at the terminals t t (one only of which is seen in Fig.
61) of the circuit, consisting of the key k, the detector D,
and the resistance box R, the current passing through the
detector will be inversely proportional to the sum of the
resistances of the key, detector, and resistance box. Such
a constant potential difference can be maintained, as will
be seen in § 13 9, page 261, by attaching to the terminals tt
Chap. IV.] CALIBRATING BY USING KNOWN RESISTANCES, 165
an accumulator or any galvanic cell, the resistance of
which is small compared with the rest of the resistance
in the circuit.
To perform the calibration, it is, perhaps, best to first
employ such a resistance in the box r that the deflection
on the detector is about 10° ; let this be r^, and let the
Fig. 61.
galvanometer resistance be g^ and let the deflection be
(P^. Next employ a resistance r.,, such that
or
n =
1^,
then the current will be doubled since the resistance of
the key k is practically nought, if the 2jlatinu7)i contact
points be cleaned hy inserting a piece of paper between
them, then pressing them together, and pulling out the
paper with the points pressed together. (Emery paper
should not be used as it rubs away the platinum, and
166 PRACTICAL ELECTRICITY. [Chap. IV.
still less should the contacts be scraped with a knife or a
file.) Let the deflection, with this value of r^, be d°^
Next employ a resistance rg, such that
or r^=lr,-^g,
then the current will be trebled. Let this produce a
deflection of d^°, &c. In this way a series of deflections
will be obtained, corresponding with currents propor-
tional to 1, 2, 3, 4, &c., and a relative calibration curve
can be drawn in the way already described.
The Wheatstone Bridge.
97. Wheatstone's Bridge. — The differential galvano-
meter, in its simple form, is a very convenient apparatus
rig. 62.
for testing the equality of two resistances, but there is a
still better method for accurately and rapidly comparing
any two resistances, which was originally devised by Mr.
Christie, and brought into public notice by the late Sir
Charles Wheatstone, and hence has been called a
^^Wheatstone's bridge,'' or a " Wheatstone's balance."
The principle of the Wheatstone's bridge is seen from
Fig. 62, and is as follows : — In passing from p to Q, either
along the wire P s Q, or along p t q, there are points having
all potentials between the potential of p and that of Q,
therefore it follows that for every point in the circuit
P S Q, there must be a point on the circuit P t q, having
the same potential. Let s and t be two such points ;
then, if they were joined with a galvanometer, no current
Chap. IV.] WIIEATSTONE's BRIDGE. 167
would flow through it, or if joined to the opposite quarter
cylinders of the electrometer described in § 75, page 130,
there would be no deflection. Let A be the current
flowing along p s, and which also must be the current
flowing along s Q, since no current passes through tho
galvanometer, and B the current flowing along P T Q, and
let a, b, c, d be the resistances respectively of p s, s Q, p t,
T Q ; then, since the potential difierence between p and s
is the same as the potential difierence between p and t,
A a = B c.
Similarly, since the potential difference between s and Q
is the same as the potential difference between t and Q,
A6 = Bd
Therefore, combining these two equations, we have
a _c
'h~'d'
which is the law of the Wheatstone's bridge.
The last equation may be written in the form
a _ h
~c ~ d '
and this is the equation that we should have obtained for
no current through the galvanometer, had its terminals
joined p and Q, and the current generator been placed
between s and t. Hence when balance is obtained ivith a
Wheatstone's bridge, the balance will not be disturbed by
interchanging tlie galvanometer and battery.
In order, then, to tell the value of one of the resist-
ances, say a, by the Wheatstone's bridge method, we must
know the value of either of the adjacent ones, say b, in
ohms, and the ratio only of the other two, say c and d.
Hence one mode of using the bridge to measure the resist-
ance of a is to keep the ratio of c to c? constant, and simply
vary the resistance of b until no current passes through
the galvanometer. Another method consists in keeping h
168 PRACTICAL ELECTRICITY. [Chap. IV.
constant, and varying the ratio of c to d. For example,
the resistances c and d may be the resistances of different
lengths of the same kind of wire, in which case we know
that c will be to d simply as the ratio of these lengths,
whatever be the absolute resistance in ohms of the two
parts. A form of Wheatstone's bridge, in which p t q, of
Fig. 62, was one piece of stretched wire, and the ratio of
c to d varied by moving the connection of the wire lead-
ing to one terminal of the galvanometer, was originally
employed by the Electrical Committee of the British
Association, and is, for this reason, sometimes called the
British Association bridge ; at other times, the " metre
bridge,'^ from the stretched wire being a metre long. The
wire may be made of platinum, or bettor still, of platinum-
iridium, which, being very hard, prevents the wire being
worn at any part.
A convenient form of metre bridge is shown in Fig. 63.
It has three stretched wires w w, each a metre in length,
and so arranged that either one of them alone, or two of
them in series, or all three in series, can be made use of
to form the two sides c and d of the Wheatstone's bridge
(Fig. 62). When the plug e is, as in the jBigure, placed in
the hole h, the current simply passes through the stretched
wire which is nearest to the observer. If on the other
hand the plug e be put in the hole A, then, since the
brass plate p is permanently connected with the plate p
by a thick copper strip under the base of the instrument,
the middle stretched wire is short-circuited, and the wire
nearest to the observer is in series with the one farthest
from him. Lastly, if the plug be removed altogether
the three wires are in series.
The object of thus lengthening the wire is to increase
the sensibility of the test when desired, and a still further
increase in the sensibility can be effected by removing the
short-circuit pieces s^ Sj, and inserting coils of known re-
sistance in place of them. For example, suppose that the
ratio of the unknown to the known resistance be f , then
the slide k must be placed so as to divide the stretched
Chap. IV.l METRE BRIDGE. 169
wire into two parts having this ratio. Hence, if one of
the three wires only be used, the lengths of the two parts
which will give exact balance will be 60 and 40 centi-
metres, and an error of 1 centimetre in the position of
170 PRACTICAL ELECTRICITY. [Chap. IV.
the slider will correspond with an error in the determina-
tion of the ratio of
^ _ 60
39 40
X 100 per cent., or 4 per cent
1-5
If, on the other hand, the three wires in series be em-
ployed, then the lengths into which the three metres of
wire must be divided to obtain exact balance will be 180
and 120 centimetres, and an error of one centimetre in
the position of the slider will correspond with an error in
the determination of the ratio of
181 180
119 120 T^^ ^ 1 .
X lUU percent., or 1-4 per cent.
1-5
If now two coils, each having a resistance equal to,
say, 1,000 centimetres of the stretched wire be inserted
in place of the short circuit pieces Sj and Sg, an error of
a centimetre in the position of the slider will only corre-
spond with an error of
1381 1380
X 100 per cent., or 0*18 per cent
Contact between the platinum-tipped knife-edge k
and one or other of the stretched wires, is produced by
depressing the knob k, which causes the lever to which
this knife-edge is attached to turn on an axis A A. On
removing the pressure, the lever is pressed up by a spring
underneath it ; and the slider should never be moved
with the knife-edge k depressed, as this would scrape the
stretched wire and alter its diameter. In order to enable
k to make contact with either the first, second, or third
wire, the knob k is not fastened rigidly to the lever, but
can slide along it in a slot, and can be so placed that
the near end of the spring S rests in either of the three
Chap. IV.] SENSIBILITY OF THE WHEATSTONE's BRIDGE. 171
grooves on the top of the lever corresponding with the
three positions of k when it is in contact with the three
stretched wires respectively.
98. Superiority of the Wheatstone's Bridge over
the Differential Galvanometer, and Conditions affecting
the Sensibility of the Bridge. — The Wheatstone's bridge
is superior to the differential galvanometer^ in that not
merely can two resistances be ascertained to be equal to
one another, but the value of any resistance in terms of
another can be exactly measured, so that if we possess one
single resistance the value of which is known exactly in
ohms, we can, without knowing the resistance of any other
wire, measure, by means of the metre bridge, the value in
ohms and fractions of an ohm of any unknown resistance.
Practically, however, the sensibility of the bridge is limited by
the galvanometer not being sensitive enough to indicate the small
current that passes through it when the ratio of a to J is not quite
equal to that of c io d (Fig. 62, page 166), and when both ratios
are far from unity. In fact it can be shown that the bridge is most
sensitive when all the four resistances, a, b, c, d, are equal to one
another. If, however, it is impossible to make them equal, then it
is desirable to consider whether the galvanometer or the battery
{see § 129, page 226) have the higher resistance, because greater
sensibility will be obtained by using the one that has the higher resist-
ance to connect the junction of the two greater of a, b, c, d, with the
junction of the two less, than if the galvanometer and battery be
joined up in the opposite way. For example, if
a = 1 ohm
b =z 100 ohms
c =: 4 ohms
d = 400 ohms,
and the resistances of the galvanometer and battery be 37 ohms
and 5 ohms respectively, one terminal of the galvanometer ought
to be connected with the junction of a and c, and the other with
the junction of b and d. {See also § 238, page 467.)
Further, it is important to consider whether we should select a
galvanometer wound with fine wire or one wound with thick wire,
hi order to obtain the most accurate measurements with a Wheat-
stone's bridge. Calculation and experiment show that if nothing
but the gauge of wire used in winding the bobbins of the galvano-
meter be varied, that is to say, if the bobbins and the space on
them occupied by the covered wire remain the same, as well aa
172 PRACTICAL ELECTRICITY. [Chap. I\.
the strength and direction of the controlling field and the suspen-
sion of the galvanometer, then with a given testing battery,
and with given values of the four " artns " of the bridge, a, b, c, d,
the greatest deflection will be produced on a galvanometer on
making a definite change in one of the four arms, say «, if the wire
wound on the galvanometer bobbin be such that the resistance
of the galvanometer equals the product of the sum of the resistances of
the two arms on one side of it into the sum of the resistances of the two
arms on the other side of it, divided by the sum of the resistances of the
four arms. For example, if the galvanometer connect the junction
of a and c with the junction of b and d, the wire used in winding
the galvanometer bobbins ought to be selected of such a thickness
that the galvanometer when wound has a resistance of
{a ^b) {c^-d)
a -\- b -\- c -\- d '
Of course this does not mean that a roughly-made pivot galva-
nometer having this resistance will give better results than a delicate
fibre-suspended reflecting galvanometer with a much greater or a
much less resistance. The formula can only be used on the
assumption that nothing but the gauge of wire employed in winding
the galvanometer can be varied. {See § 237, page 466.)
99. Commercial Form of Wheatstone's Bridge. —
In the Wheatstone bridges, as commonly constructed,
the resistances of all three branches are made up of
coils, the values of which are known in ohms, and the
apparatus is frequently made of the form shown in Fig.
64, where the c and d of Fig. 62 are each replaced by
three coils of 10, 100, and 1,000 ohms, called the ^^pro-
portional coils" and the b of Fig. 62 is made up of the
following coils, 1, 2, 2, 5, 10, 10, 20, 50, 100, 100, 200,
500, 1,000, 1,000, 2,000, 5,000. With these latter six-
teen coils, any integral resistance between 1 and 10,000
may be formed, and this special arrangement, although
not requiring the least number of coils to enable any
resistance between 1 and 10,000 to be obtained, is found
in practice to be the most convenient. With this bridge,
then, we can measure any resistance between y^io ^ ^y
or YYx*^ ^^ ^^ ^^^> ^^^ m- ^ 10,000, or one million
one hundred and ten thousand ohms.
In Fig. 64, the battery seen at the left-hand side
is indicated symbolically by three thin Lines, which stand
Chap. IV- 1 COMMERCIAL FORM OF WHEATSTONE'S BRIDGE.
173
for the copper plates, and by three shorter and thicker
lines, which stand for the zinc plates or rods. The cells
are understood to be coupled by the zinc plate, or rod, of
the upper cell being joined to the copper plate of the
second, and the zinc plate of the second to the copper
plate of the third ; so that the six lines in Fig. 64 are a
symbolical representation of the battery shown in the
next figure (Fig. 65). This symbolical representation,
Fig. 64.
which is commonly used to stand for a battery, will be
employed in the rest of this book, and will be found still
further explained in § 135, page 240.
The resistance coils sold in boxes are always made
so that the resistance of each is an exact number of
ohms or certain special fraction of an ohm at the same
temperature, which is specified on the box, and the
trouble of adjusting a number of coils to fulfil this con-
dition causes resistance boxes to be rather costly. It is
undoubtedly more convenient that the resistance of each
coil should be an exact number of ohms or a certain
174 PRACTICAL ELECTRICITY. [Chap. IV.
special fraction, but it would be far cheaper if the coils
were made approximately to have the resistance 1, 2, 5
ohms, &c., and their actual resistances in ohms and frac-
tions of an ohm, when tested at some one temperature,
were marked on the box.
100. Bridge Key. — In using a Wheatstone's bridge it
is desirable to send the current through the four arms of
the bridge a, b, c, d (Fig. 62), before it is allowed to pass
through the galvanometer, and this is especially impor-
tant when testing the resistance of the copper con-
ductor of a long submarine cable, since the current in such
a case takes an appreciable time to reach its maximum
value and become steady, due to the cable acting as a
^^ co7idenser " (see § 162, page 301). Hence, if the galva-
nometer circuit were completed when the battery was
attached to the bridge, an instantaneous swing of the
galvanometer would be produced, even if a bore to b the
ratio of c to d. And although, since the ratio of re-
sistances having been effected, the deflection of the galva-
nometer would become nought as soon as the current in
the four branches of the bridge became steady, great
delay in the testing would be caused by this first swing
of the needle. A similar difficulty would occur in
measuring the resistance of an electromagnet or even of
any coil without an iron core, if it were not wound doubly
as are the coils in resistance boxes (see Fig. 7, page 28) ;
because whenever a coil is so wound that a current pass-
ing through it produces magnetic action, a short interval
of time has to elapse, after putting on the battery, before
the current reaches its maximum, or steady, value, arising
from what is called the " self-induction " of the coil.
A key for sending the current through the four
arms of the bridge before it is allowed to pass through
the galvanometer, is shown at k (Fig. 65), and is a
modifi.cation of the one originally employed by the Elec-
trical Committee of the British Association. On press-
ing down the button, contact is first made between the
flexible piece of brass a and the flexible piece of brass b.
Chap. IV.]
BRIDGE KEY.
175
This completes the battery circuit, and causes the cur-
rent to flow through the four arms of the bridge shown
symbolically in Fig. 65 by the spiral lines. On the
button being still further pressed down, b is brought
into contact with a little knob of ebonite e on the top
of the flexible piece of brass c. This does not complete
Fig. 65.
any other electric circuit ; but on the button being still
further depressed, c is brought into contact with d, and
the galvanometer circuit is completed.
This form of key is to be preferred to the ordinary
bridge key, because all the connections are above the
base of the key and in sight, whereas when the connec-
tions are made under the base, it frequently happens
that the pieces of guttapercha-covered wire used to
make the connections are either badly insulated, or are
loosely connected at their ends with the terminals of the
key, and so introduce unnecessary resistance.
176 PRACTICAL ELECTRICITY. [Ohajk IV.
101. Use of a Shunt with the Bridge. — It is desirablft
to employ also another key k (Fig. 65), which may
be quite simply made of a twisted bit of hard brass wire,
bent so as to press up against a sort of bridge of hard
brass wire, since the resistance at the contact is in this
case of no consequence. When the key is not depressed,
a portion of the current is shunted past the galvanometer
through any convenient shunt «, the resistance of which
need not be known, as it does not enter into the calcula-
tions. The object of this shunt is merely to diminish the
sensibility of the galvanometer when the first approxi-
mation is being made to the value of the unknown re-
sistance. As soon as this has been done the key k should
be depressed, and all the current in the galvanometer
circuit arising from want of perfect balance allowed to
pass through the galvanometer itself, and the resistances
adjusted until perfect balance is obtained. Another de-
vice to expedite the testing, and also to prevent power-
ful currents being sent through the galvanometer, consists
in not holding the key k down when the first rough
approximation is being made, but merely giving it a tap,
which has the effect, when the balance is far from
perfect, of giving the needle of the galvanometer a slight
impulse to one side or the other, according as the ratio
of a to 6 is larger or smaller than that of c to d, instead
of causing the needle to violently swing against the stops
on one side or the other as it would do if the key k were
held down before balance was arrived at.
102. Meaning of the Deflection on a Bridge Galva-
nometer.— A considerable amount of time will be saved
in testing if the meaning of a deflection of the galvano-
meter needle, say to the right, be once for all definitely
ascertained, and a note be made whether it means that the
ratio of a to 6 is too large or too small. The simplest
way of recording this, if we assume, for example, a to
be the unknown resistance, is to put the words ^^ in-
crease h " and " diminish h " one on each side of the gal-
vanometer, these being the directions to be followed
Chap. IV.] SHUNTS. , 177
according as the needle deflects towards one or other of
them. The position of these two directions must, of
course, be reversed if the terminals of the testing battery
be reversed.
Shunts.
103. Shunts. — We have already seen, for example, m
the apparatus shown in Fig. 17, page 59, and again when
using a Wheatstone's bridge (§ 101, page 176), that it is
sometimes convenient to use a wire as a by-path or shunt
to convey a portion of the current, the remainder only
passing through the galvanometer. We will now consider
what must be the relative resistances of the shunt and
galvanometer to allow any particular fraction of the whole
current to pass through the galvanometer. Let s, g be
the resistances in ohms of the shunt and galvanometer,
and S, G the currents in amperes passing through them
respectively ; then, if Y be the potential difference in volts
at the terminals of the shunt and galvanometer, it fol-
lows from Ohm's law (§ 74, page 130) that
s = -^.
8
9
or the current strengths in the galvanometer and shunt
are inversely as their resistances.
Also, by a well-known rule in proportion, it follows
that
G 8
S + G~iTV
and S g
sTg ^ s^g'
but S + G is the sum of the currents flowing through the
178 PRACTICAL ELECTRICITY. [Chap. IV.
shunt and the galvanometer respectively, and therefore is
equal to the whole current in the circuit, A amperes say,
hence
G- 8__
A " « + /
and S g
A" s + g
104. Multiplying Power of a Shunt. —
Since . s 4- a ^
A = -T^ X G,
8
, 8 -^ g
the fraction is frequently called the " multiplying
power of the shunt" that is, the quantity that the cur-
rent flowing through the galvanometer must be multiplied
by to obtain the total current.
As an example of the last equation, let us suppose
that we desire that G shall be one-tenth of A, then
8 + g lo'
1
or 8=-g;
or, again, if we wish that G shall be one-thousandth of A,
then
_s 1_
s + g~ 1000 '
1
105. Combined Resistance. — It would be, of course,
possible to substitute for the two resistances s and g^
which are in parallel, a single wire of resistance x such
that for the same potential difference^ V, at its terminals,
the current flowing through it should be equal to the sum
of the currents flowing through the two parallel circuita
Chap. IV.] COMBINED RESISTANCE. 179
To find X we have
V
the current that would flow through it = — i
V
the current flowing through 8 , . = — >
V
the current flowing through g . . = — »
V V V
, •. since — = J 9
X s g
sg .
s -\- g
or if two wires be in parallel, then the product of their
resistances divided by their sum represents the resistance
of a single wire through which a current will pass, equal
to the sum of the currents passing through the two wires,
for the same potential difference. Such a single resistance
is called the ^^ combined resistance" or the "parallel
resistance" of the two.
From what has preceded we see that when G is a
tenth of A,
sg 1
s + g-lO
or the combined resistance of the shunt and galvanometer
is one-tenth of the resistance of the galvanometer.
In the same way, if there be any number of resistances
a, b, c, d, &c., in parallel, and a; be a single resistance,
such that with the same potential difference at its termi-
nals the current that will flow through x is equal to the
sum of the currents that flow through all the resistances
a, 6, c, rf, &c., the combined resistance
Wt-\-',*'-
180 PRACTICAL ELECTRICITY. [Chap. I V-
If A, B, 0, D, &c., be the currents flowing through
the various circuits, and X be the total current, then
A a
abed
1
&c.
Example 38. — What must be the resistance of a shunt
so that f of the whole current shall pass through a galva-
nometer having 452 ohms' resistance 1
Here 8 4
8= ig.
Answer. — 1,808 ohms.
Example 39. — If the resistance of a shunt be 1 ohm,
and that of the galvanometer 2 ohms, what fraction of the
total current passes through the galvanometer and what
through the shunt 1
We have — = ,
A « + ^
therefore, substituting the values given,
G _ 1
A~3-
Answer. — One-third of the current passes through the
galvanometer, and two-thirds through the shunt.
Example 40. — If a galvanometer have 1,980 ohms'
resistance, and a shunt be attached so that the current
passing through the galvanometer is only xJ^th of the
Chap. rVO CONSTRUCTION OF A SHUNT BOX. 181
total current, what will be the resistance of the shunt,
and by how many ohms will the resistance of the circuit
be diminished by employing the shunt ?
Here s 1
or, in this case, = 20 ohms;
s g
and —, — = 19-8 ohms ;
. *. the diminution of the resistance of the circuit pro-
duced by applying the shunt is 1,980 - 19*8, or 1,960-2
ohms.
106. Construction of a Shunt Box. — The three coils,
having respectively the |^th, /^^th, and -^Jg*^ ^^ ^^^ ^^6-
sistance of the galvanometer, are usually inserted in a
small box h (Fig. 66), which accompanies the galvanometer.
The terminals of the galvanometer, as well as the two wires
which connect the galvanometer with the rest of the cir-
cuit, are joined to the binding screws s s on the shunt
box, and each of the three shunt coils has one of its ends
connected with the brass piece c, while the other ends
are connected respectively with the brass pieces d, e, and
p. If, then, the brass plug p' be inserted in the hole be-
tween the brass bar A B and the brass piece c, all the
current will pass from A b to c, through the plug, and
none through the galvanometer, since the resistance of
A B to c through the plug is extremely small compared
with that through the galvanometer. If, on the other
hand, the plug be inserted in the hole between a b and d,
as in the figure, the current will pass from A b to d
through the plug, and from d to c through the coil in
the shunt box, which connects with c. And as this coil
has ^th of the resistance of the galvanometer, y^th of the
total current will pass through the galvanometer. Simi-
182 PRACTICAL ELECTRICITY. [Chap. IV,
larly, if the plug be inserted in the hole between a b and
E, or A B and f, xootli or xoVoth of the whole current will
pass through the galvanometer.
Tn order to obtain very good " surface insulation "
{see § 140, page 267), the brass pieces A, b, c, d, e, and f are,
Pig. 66.
in the particular shunt box shown in the figure, mounted
on ebonite pillars p, p, p, p, and to avoid the insertion of the
plug into one or other of the holes pushing these pillars
outwards, and so preventing the plug making firm contact
with the pieces of brass on each side of it, there is a
spring cap c c, sliding on the plug, which passes over the
two vertical pins on each side of the hole, and so holds
Chap. IV.l USING A SHUNT INCREASES TOTAL CURRENT. 183
the brass pieces together against the wedging action
which tends to force them asunder when the plug is pressed
in. The plug has a long ebonite handle i, which should
be held by the flat part at the end to prevent leakage
taking place along the surface of the handle and through
the body of the experimenter to the ground.
107. Increase of the Total Current produced by the
Employment of a Shunt. — The Use of Shunts with a
Differential Galvanometer. — The insertion of a shunt
S Q
diminishes the resistance of the circuit from a to — r^ •
In some cases this produces practically no effect on the
total current, so that the current flowing tlirough the
8
galvanometer will be — — — of the current that was flow-
ing through it before the insertion of the shunt. But in
other cases this variation of the resistance in circuit ma-
terially affects the total current, so that, although G is
8
always — - — of the total current, this total current may
be so increased by the diminution of the total resist-
s
ance that the fraction — ; — of the new total current is
8 -¥9
practically as large as the previous total current, or, in
other words, shunting the galvanometer may produce prac-
tically no diminution in the current passing through it.
This effect produced on applying a shunt, which
is often entirely overlooked by beginners, may be ex-
perimentally investigated with the apparatus shown in
Fig. 67. B is a battery consisting of six cells fitted with
terminal binding screws, so that one, two, or any number
of cells up to six can be used ; m is a galvanometer of
very small resistance, and R^, Rg, R3, R4, resistance coils
in the main circuit, g is a galvanometer of some 500
ohms' resistance, also in the main circuit, but fitted with
a shunt s. Any one of the coils, Rj, Rg, R3, or r^, can be
cut out of circuit by turning the handle h so that a small
184
PRACTICAL ELECTRICITY.
rChap. IV.
bridge-piece h of flexible brass makes contact between two
metallic buttons k k, which are attached respectively
to the two ends of the coil.* The resistance in the shunt s
can be varied either by taking out or inserting the plugs
in its base in the usual way, or by turning the handle
which varies the resistance in a way to be explained a
little farther on. Then it is found that if the resistance
in the main circuit is fairly large, say 1,000 ohms, alter-
ing the resistance of s alters the deflection of G, but does
Fig. 67.
not sensibly alter that of m ; while, on the other hand, if
the resistance in the main circuit is small, that is, if the
four bridge pieces at the tops of the four coils are turned
so as to short-circuit all the four coils, then the value of
s may be altered within wide limits without altering the
value of the deflection of g, but the deflection of m will
be large when the resistance in s is small, and small when
the resistance in s is large. It is necessary to be able to
vary the number of cells from one to six in order that
* This plan of cutting out a coil was the one originally em-
ployed by the late Sir Charles Wheatstone with the earliest forms of
resistance coils.
Chap. IV.l SHUNTS WITH DIFFERENTIAL GALVANOMETER. 1 85
in all the experiments, each made with a particular value
of the resistance in the main circuit, and for a series of
values of the shunt, the largest deflection of G, which is
obtained when the galvanometer is unshunted, may be
about the same.
We have merely referred to the two extreme cases,
a very large and a very small resistance respectively in
the main circuit ; but readings should be taken of the
deflection of G for a series of values of the resistance of
the shunt, with each of several values of the resistance in
the main circuit ; and a series of curves should be drawn
connecting deflections of G with values of s, each curve
for a different resistance in the main circuit.
The mathematical working out of this experiment,
together with the consideration of the construction of
" constant total current shunts ^^^ will be found farther on
(§ 137, page 253).
We have seen (§ 87, page 149) that if the two coils c
and c' (Fig. 59) of the differential galvanometer have
equal resistances, and if, in addition, they be so adjusted
relatively to the needle that no deflection is produced
when equal currents flow round the coils, no deflection will
be produced when A and b have equal resistances, and a
difference of potentials is set up between p and q by any
convenient current generator. If, now, one of the coils,
say c, be shunted with a shunt, having, say, one-ninth of
the resistance of c, then the parallel resistance of c and
its shunt will be one-tenth of the resistance of c alone.
Therefore if the resistance of a be also diminished to one-
tenth of what it was, the total resistance of the branch
p A c Q will become one-tenth of what it previously was,
hence ten times as much current will pass through A and
through B, but of this larger current only one-tenth part
will pass round the coil c, and, consequently, there will
still be no deflection of the needle. We can generally
conclude that if one coil, c, having a resistance g ohms, of
a differential galvanometer be shunted with a shunt of 8
ohms, no deflection will be produced when
186 PRACTICAL ELECTRICITY. [Chap. IV.
resistance of A _ s
resistance of B ~ s + ^
If, therefore, we have a box of resistance coils, the
resistance of which can be varied from, say, 1 to 10,000
ohms, we can, by the addition of a tenth shunt to one of
the coils of a differential galvanometer, measure resist-
ances varying between 0"1 and 100,000 ohms.
108. Sliding Resistance Boxes. — The resistance box
8 (Fig. 67) is different from any of the forms used in
the previous experiments. Fig. 68 shows this resistance
box in plan, and from that it will be seen that there
are two ways of altering the resistance, the one by
inserting plugs into the holes between p and Q, or
by removing these plugs in the manner previously de-
scribed, the other by turning one, or both, of the slid-
ing handles h h. Turning these handles can be effected
without looking at the box, and hence such sliding
resistance boxes are commonly employed for " duplex
telegraphy" or the sending of two messages simulta-
neously, in opposite directions, along one telegraph wire,
in connection with which the signaller requires to vary
the resistance without having to take his attention off
the message he is sending or receiving.
Between each pair of adjacent studs Sj, Sg, S3, &c., in
one half of the box are coils, each having the value of 40
ohms, while between each pair of adjacent studs s^, Sg, Sg,
&c., in the other half of the box are coils, each having the
value of 400 ohms. Hence, with the arms in the positions
shown in the figure, the current entering at the binding
screw T has first to pass through as many of the coils
between p and Q as are unplugged, next through eight
coils, each of 40 ohms, then from the arm h to the arm h,
and lastly through five coils, each of 400 ohms, and out
by the terminal t In addition, therefore, to any re-
sistance that may be unplugged between p and Q, there is
a resistance of 2,320 ohms in circuit.
Resistance boxes with sliding arms are much
Chap. IV.] SLIDING RESISTANCE BOXES. 187
cheaper to construct than plug resistance boxes, as the
labour and expense of grinding the plugs into the coni-
cal holes is saved. As, however, it is very difficult to
avoid an unknown small resistance being introduced at
the contact of a stud and the revolving arm, well-made
plug resistance boxes are far better for accurate work.
109. Measuring a Resistance during the Passage
of a Strong Current. — In cases where a conductor is
warmed by the passage of a strong current, and so has
its resistance altered, it is not sufficient to know what
the resistance of tlie conductor was when cold, but we
must know what it is while the current is jmssing through
it. This cannot, of course, be done with a Wheatstone's
188 PRACTICAL ELECTRICITY. [Chap. IV.
bridge or a differential galvanometer, but an approxi-
mation to the true resistance can, in some cases, be made
by stopping the current that was passing through the
conductor, and then measuring, as quickly as possible, its
resistance with a Wheatstone's bridge or differential
galvanometer in the ordinary way (see § 97, page 167).
This, at the best, can give but an approximation, and
when the conductor cools very rapidly on the stoppage
of the current, as, for example, in the case of the fila-
ment of an incandescent lamp, the result so obtained
would differ very seriously from the true value. Further,
this method could not be employed at all when it is
desired, for example, to measure the resistance of an
" electric arc," that is, the intensely heated space between
the carbon points in an *' arc lamp," because the arc
ceases to exist immediately the current producing it is
stopped.
In such a case, the following method must be em-
ployed. By means of an electrometer, or a voltmeter
V (Fig. 69), measure the potential difference, in volts,
at the ends of the conductor c, whose resistance we desire
to know, and simultaneously measure with an ammeter
the current A, in amperes, passing through the con-
ductor ; then, if o be the unknown resistance of c in
ohms, we have, from the definition of resistance,
V
This method can, of course, be employed in all cases,
but is especially useful when a conductor has a fairly
strong current passing through it, and we desire to
Chap. IV.] RESISTANCE WITH A STRONG CURRENT. 189
measure the resistance of the conductor while this strong
current is passing through.
If the instrument used to measure the potential
difference be an electrometer, through which no current
passes, the deflection of the ammeter will measure the
true current passing through the conductor only ; but, on
the other hand, if a voltmeter be employed, through
which some current passes, then it must not be forgotten
that the current passing through the ammeter is the
sum of the currents passing through the conductor c and
the voltmeter. As a rule, this will not introduce any
serious practical error, as the resistance of the voltmeter
being very large compared with that of c, the current
Fig. 70.
passing through the voltmeter is very small compared
with that passing through c. If, however, this be not
quite the case, on account of the resistance of c being
large, then the current passing through the voltmeter
must be subtracted from that measured by the deflec-
tion of the ammeter to obtain the value of A in the
above formula. Or, more simply, interrupt the volt-
meter circuit and now observe the ammeter reading.
If, however, the resistance of c be large, the making
and breaking of the voltmeter shunt circuit may very
possibly alter not merely the current passing through
the ammeter, but even that passing through c, so that the
reading given by the ammeter when the voltmeter shunt
circuit is broken, although indicating quite accurately
the current the7i passing through c, would not give the
amount that was passing through c when the voltmeter
reading was taken. Therefore, from these two observa-
tions the resistance of c could not be accurately deter-
190 PRACTICAL ELECTRICITY. [Chap. IV.
mined, unless the resistance of the voltmeter were known,
and the current passing through it calculated and allowed
for. In such a case it is better to make the voltmeter
a shunt to both the ammeter and c, as shown in Fig. 70 ;
for, with this arrangement, the resistance of c, plus that
of the ammeter, will be correctly found, and if the re-
sistance of the ammeter be either small compared with
that of c, or if it be correctly known, then the resistance
of c can also be found by a simple subtraction.
The determination of the resistance of a battery by
means of simultaneous readings on an ammeter and
voltmeter will be found described in § 1 1 6, page 205.
110. Ohmmeter. — The necessity of observing two
0 ^ —
Fig. 71.
instruments at the same time is a disadvantage in the
employment of the method of testing just described, and
hence the following instrument, called an " ohmmeter^'"
was devised by the author for measuring, by a single
observation, the resistance of any part of a circuit through
which a strong current is passing. The ohmmeter con-
tains two coils acting on the same soft iron needle ; one
of these coils, c C (Fig. 71), attached to the terminals t t
(Fig. 72), is made of a short piece of thick r/ire, and is
placed in series with the resistance o to be measured ;
while the other, c c (Fig. 71), attached to the terminals
tt (Fig. 72), is composed of very fine wire, and is put
Chap. IV.") OHMMETER. 191
as a shunt to the unknown resistance. Hence the main
current A produces its effect by means of the thick wire
coil, and the difference of potentials Y at the terminals
of the unknown resistance by means of the fine wire
coil ; these coils are placed at right angles to one another,
and in consequence of this, it may be shown that the action
on the needle is due to the ratio of V to A, that is, to
the value of o. When no current is passing through
Pig. 72.
either coil the needle will rest in any position, but on
sending a current through the thick coil alone the
pointer at once moves to nought. And by properly pro-
portioning the shapes of the coils, and by winding the
wire on them in a definite way, it is possible to make
the angular deflection of the needle from the zero
position directly proportional to the resistance o. The
thick wire coil may be always kept in the main cir-
cuit, or in any branch circuit, then on attaching the
terminals tt to any two points on the same circuit by
means of wires the needle will at once move to a
number on the dial, which will indicate the resistance
192 PRACTICAL ELECTRICITY. [Chap. IV.
in ohms at the time in question of that part of the
circuit between the two points.
On account of the alteration of resistance by heating,
it is very difficult, unless very thick German silver wire is
employed, to construct resistance coils for use with strong
currents, so that the resistance shall not be changed by
the passage of the currents. But the use of an ohm-
meter permits the employment of an iron wire, or even
of a bit of wet rope, as a temporary resistance for ex-
perimental pui-poses, the resistance of the iron wire or
of the wet rope being determined with the ohmmeter at
the moment the experiment is being made.
Heat Generated and Work Done by an Electric
Current.
111. Amount of Heat Generated by an Electric
Current. — When considering the effects produced by a
current earlier in the book, we saw that the rise of
temperature of the calorimeter in a given time was not
proportional to the current strength. We will now
examine this more fully, and for doing this the
apparatus shown in Fig. 73 may be conveniently
employed. It consists of a coil of German silver wire
dipping into a small metal vessel of paraffin oil, the
temperature of which can be observed by means of a
delicately graduated thermometer t, the bulb of which
dips into the oil. T is supported by an indiarubber
stopper, through which it passes, and which itself fits
into a small wooden cap, seen in the figure, which
forms the top of the vessel containing the paraffin
oil. This little vessel is supported in the middle of a
very much larger metal vessel, seen in the figure,
made with double sides, double top, and double bottom,
the space between the two being filled with water. This
water jacket, as it is called, is for the purpose of pre-
venting heat passing from the body of the experimenter,
or from any adjacent lamp, into the paraffin oil, which
would interfere with the experiment, seeing that our
Chap. IV.I HEAT GENERATED BY A CURRENT.
193
object is to measure the heat produced in the vessel of
paraffin oil solely by the current passing through the
coil of German silver wire immersed in it. It might, at
first sight, appear that the simplest plan of avoiding this,
as well as of avoiding the loss of heat from the vessel
Fig. 73.
of paraffin oil, would be to surround it by a sort of coat
of cotton- wool or of fur. As, however, it is impossible to
TYiake such a coat which shall prevent all loss of heat,
there being no insulators for heat (see § 93, page 159), and
as this loss, although small, would be vague in amount, it
is better to allow a greater loss provided that tJie loss is
known in amount ; this result is obtained by using a
water jacket, and by maintaining this water jacket at
N
194 PRACTICAL ELECTRICITY. fCbap. IV.
constant temperature, which can be tested by means of
the thermometer t' dipping into the w-ater of the jacket.
The two wires to the left side of the figure go to the
current generator, which, on pressing down the key,
sends a current through the coil of wire in the calori-
meter, the galvanometer, and a longer or shorter
portion of the stretched wire shown at s in the figure.
The length of this stretched wire put in the circuit can
be regulated by a loose flexible wire, not shown in the
figure, which is attached at one end to the free binding
screw of the galvanometer, and at the other end to one
of the binding screws s.
It will be seen that in the experiments shown in
Figs. 6, 15, and 73, the current strength is varied by
inserting a shorter or a longer length of wire in the
circuit, whereas in the experiments shown in Figs. 17
and 20 the same result is much more simply attained
by altering the distance between two zinc plates, or
rods, dipping into a small quantity of a saturated solu-
tion of zinc sulphate. The reason of this is that in the
first and third experiments the current must be kept
quite constant for a minute or so while the gas is
being steadily generated in the first case, and the heat is
being generated in the calorimeter in the third, where-
as in the last two experiments it is only necessary
to keep the current constant just long enough to take
a reading of the galvanometers. Now it would be
somewhat difficult to maintain a current quite constant
for some little while by means of plates dipping into
liquid, unless some plan of fixing the plates in any par-
ticular position were employed ; and even then, as will
be seen later on, a liquid resistance would not be as
constant in value as that produced by a given length
of v/ire. Hence the latter plan should always be
adopted when it is necessary to maintain the current
constant for any length of time.
In Fig. 73, M is a controlling magnet, and, as
already explained, if m be placed Tiear the galvanometer,
Chap. IV.] iJEAT GENERATED BY A CURRENT. 195
the latter must be calibrated with M in the same position
as it is in when the galvanomc 'er is used, since
changing the position of a magnet when it is near a
galvanometer not only alters the absolute, but generally
also the relative calibration curve.
To carry out the heating experiment, a certain
current is allowed to pass through the apparatus, and
the deflection on the galvanometer is observed. The
current being kept constant, the time rise of tempera-
ture of the liquid in the calorimeter is measured by the
thermometer T, the liquid being kept constantly stirred
with the stirrer r to prevent its becoming hotter in one
part than in another. The time rise of temperature
is obtained by making a series of simultaneous observa-
tions of time and temperature ; for example, successive
observations of the thermometer may be made by one
observer at times which are noted on a watch by another.
A curve can now be drawn having its abscissae, or
distances measured along one line, proportional to the
times measured from the instant of closing the cir-
cuit, or better, from the instant that the first observation
of temperature is made after the current has become
steady, and its ordinates, or distances measured along a
line perpendicular to the former, proportional to the
temperature at the ends of each of the periods of time.
From this curve, which experiment shows to be concave
to the axis along which time is reckoned, the tempera-
ture of the thermometer t at any instant of time, or the
rise of temperature during any interval of time, can be
seen. This time rise of temperature curve does not, how-
ever, represent the time production of heat, sinc^
while the calorimeter is gaining heat from the coil in
it through which the current is passing, it is losing heat
on account of radiation and convection* Now it is the
* Radiation is the transference of heat from one body to another
without the intervening space becoming warm, as, for example, the way
in which the sun warms the earth ; conduction is the transference of
heat from one part of a body to another, due to all the intervening
196 PRACTICAL ELECTRICITY. [Chap. IV.
rate of production of heat that we want to ascertain,
not the time rise of temperature, which, without alter-
ing the current strength, or the coil through which it
is passing, or the liquid in which the coil is placed,
can be made greater or less by diminishing or increas-
ing the facility of the liquid for cooling.
112. Cooling Correction of the Observed Rise
of Temperature Curve. — Hence we must make ex-
periments and ascertain the amount of heat that was
lost while the temperature was rising, and this may
be done with great accuracy by stopping the current
and observing the time fall of temperature^ since the
calorimeter is now, while cooling, surrounded by the same
body at the same temperature as it was while it was
being warmed. From observations on the time fall of
temperature, a time cooling curve, which will be found
convex to the axis along which time is reckoned, can
be constructed. This second curve must be used to
correct the first, and so to obtain a third curve in-
dicating what the rise of temperature would have
been had there been no loss of heat. To obtain this
third curve divide the time into a number of small equal
intervals ; then, starting from the lowest part of the
heating curve, observe what was the observed rise of
temperature in the first short interval of time ; next,
referring to the cooling curve, observe what was the
observed loss of temperature in the same interval of time
and for about the same value of a mean temperature.
This observed rise and observed loss must then be
added together, and the sum will measure what the rise
of temperature would have been during the first interval
of time had there been no loss of heat. This gives us a
new point indicating what the temperature would have
portions of the body becoming necessarily warmed, as, for example, the
way in which, when one end of a cold iron poker is inserted in the
fire, the other end gradually becomes warmed ; convection is the
transference of heat from one place to another by the bodily con-
veyance of heated liquid and gas ; as, for example, the way in w^hicb
the top of a chimney over a lighted fire becomes warm.
si
Chap. TV.] CORRECTION FOR COOLING. 197
been Lad there been no cooling. Do the same for
the second, third, fourth, &c., intervals, and add what
the rise in temperature during each interval would
have been without cooling to what the temperature would
have been at the commencement of that interval without
cooling.
In examining this third curve we find that it is a
straight line, which means that for a constant current
the amount of heat produced in every second would,
were there no loss of heat, be able to raise the tempera-
ture by the same amount. Hence the amount of heat
actually produced in every second is a constant quantity,
and this constant rate of production is measured by
the tangent of the angle between this line and the line
along which time is measured.
Next vary the current by changing the length of the
wires (Fig. 73) in circuit, which, as stated above, is
done by connecting the free terminal of the galvano-
meter with a different binding screw at s, and obtain the
corrected curve as before. On comparing the slopes of the
straight lines so obtained from the two experiments, it will
be found that they are not proportional to the respective
current strengths as measured by the galvanometer, but
to the squares of the current strengths. And the same re-
sult will be obtained if any other two current strengths
be employed in the experiment. We conclude, therefore,
from this experiment, that the heat generated in a con-
ductor hy a current in a given time is proportional to the
square of the current strength, or simply to the square
of the current*
113. Measuring a Current by the Rate of Pro-
duction of Heat. — This method of measuring the rise
of temperature by the heat generated in a coil of wire
may be conveniently employed when the currents are
so strong as to raise the temperature several degrees
* In practice it is found best to take the observations on cooling at
the end of the experiment, after the complete series of observations
of the heating produced by the various currents has been carried out.
198 PRACTICAL ELECTRICITY. [Chap. IV.
in a time so short that in it no appreciable loss of
heat can occur, since in that case the two currents will
be simply proportional to the square roots of the ele-
vations of temperature in the same time, and no cooling
experiments need be made. And the method is espe-
cially useful when we desire to measure an " alternating
current" that is, a current the direction of which is being
rapidly reversed, since in such a case neither a voltameter
nor a galvanometer with a controlling permanent magnet
can be used to measure the current strength. As to the
voltameter, the compound gas, of which we measured
the volume in the experiment described in § 3 and
§ 12, was, as seen from the experiment described in § 7,
composed of hydrogen steadily given off at one of the
platinum plates, and oxygen steadily given off at the
other, so that if the current were rapidly reversed many
times a minute, a little hydrogen would first be formed
at one of the plates, then a little oxygen at the same
plate, which, combining with the hydrogen previously
formed, would re-form water, so that on the whole
no gas would be produced^ which could be collected and
measured.
If the coil of wire, having a resistance of o ohms
in the vessel in Fig. 73, be replaced by another coil of
wire having a different resistance of o' ohms, it will be
found that for the same current and for the same quantity
of liquid in the calorimeter, the corrected elevations of
temperature in the two cases in the same time, which are
proportional to the amounts of heat produced, will be
in the ratio of o to o'. Combining this with the result
previously obtained with different currents flowing
through the same coil, it follows that the heat generated
in a conductor by a current in a given time is propor-
tional to the product of the square of the current into the
resistance of the conductor.
If the water equivalent of the calorimeter, that is,
the weight of water that is raised as much in tempera-
ture as is the calorimeter with its contents by the addi-
Chap. IV.] HEAT GENERATED IN A CIRCUIT. 199
tion of the same amount of heat, be determined, we can
measure the actual amount of heat produced per minute
by a given number of amperes flowing through a given
number of ohms. And experiment shows when the
unit of heat is taken as the amount of heat that will
raise 1 lb. of water from 0° 0. to 1° C, that A amperes
flowing through r ohms produce per minute 0'0315 A'^r
units of heat, or, generally, if H be the number of units
produced in t minutes,
H = 00315 A2r«.
If we take as the unit of heat the heat required to
raise one gramme of water from 0° C. to 1° C, and if t be
measured in seconds, then
H = 0-239 A2r<. ^
114. Work done in an Electric Circuit. — If two
conductors at difierent potentials be joined by a wire,
electricity will flow from the one of higher potential tc
that of lower as long as any potential difference exists
between them, exactly as, when a reservoir containing
water at a higher level than the surrounding country
has an opening made in the bottom of it, water will flow
out of the reservoir from the higher to the lower level
until all the water has fallen to the same level. In
order, therefore, to keep up a ^constant electric current we
must employ a machine that will transport electricity
from a place of low to a place of high potential, just as, to
keep up a steady stream of water, we must have some
machine or pump, or it may be the evaporating power
of the sun, to keep raising the water from a low to a high
level. With any such pump a certain portion of the
power expended on it would be spent, not in actually
raising water, but in overcoming the friction opposed by
the channels inside the pump to the passage of the water,
and the portion of the power so spent would be con-
verted into heat, so that the work the water could do in
falling would be less than that spent on the pump by the
200 PRACTICAL ELECTRICITY, [Chap. IV
amount that had been wasted in heat in the pump.
Consequently, the number of feet to which a pump
could raise a pound of water would be less than the
number of foot-pounds of work expended on the pump
to raise the pound of water, and experiment shows that
this difference would be greater the more quickly the
pound of water was raised.
Now a generator of an electric current, for example, a
galvanic battery, a dynamo machine, a magneto machine,
or a thermopile, is employed for the same sort of object
as a pump, viz., to raise electricity from a low to a high
potential, in opposition to the tendency the electricity
apparently possesses to flow from a place of high to
a place of low potential. The work the electricity so
raised in potential can do per second, or per minute,
in the external circuit, in the form of an electric cur-
rent, may be partly done in turning an electromotor,
or may be partly done in decomposing the substances
in a voltameter, but in both cases a portion must
be done in heating the external circuit ; or the whole
of the work may be done in merely heating the external
circuit, and since we know from the experiment de-
scribed in § 113, page 198, that the heat generated by the
current is proportional to the product of the square of
the current into the resistance, it follows that, when
all the work done in a circuit is done in the form of
heat, the total work done is proportional to the square of
the current into the resistance. But we also know that
in this simple case the current is proportional to the
potential difference at the terminals of the generator
divided by the resistance of the external circuit. Hence,
in this case, the work must be proportional to the pro-
duct of the current into the potential difference.
To express this result numerically, let the current A
be measured in amperes, the potential difference V in
volts, the resistance r in ohms, the work W in foot-
pounds, and the time t in minutes. Then, since, as we
have already seen (§ 113, page 199) that H, the heat
Chap. IV. I WORK DONE IN A CIRCUIT. 20)
generated, equals 0-0315 A^rt^ and since Joule hag
shown that the quantity of heat required to raise 1 lb.
of water from 0°C. to 1°C. (that is our unit of heat) L««
equivalent to 1,400 foot-pounds of work, it follows that
W= 1,400 X 0-0315 A2r<
= 44-25 A.^rt.
Also we know that when all the work done in the circuit
is expended in producing heat,
A=I,
r
.-. W= 44-25 AV«.
And this result is true in all cases whenever a steady
current flows through any circuit, whether it consist of
merely a resistance or, in addition, of an electromotor, or
of both an electromotor and a voltameter in addition to
mere resistance. Consequently, whenever a steady cur-
rent of A amperes flows through a circuit, at the terminals
of which V volts are maintained, the work done in foot-
pounds per minute is 44-25 AV, and the horse-
7 . . 44-25 _^ AY
power expended on the circuit — -— — ■ AY, or — -r , or
^ ^ 33,000 ' 746
0-00134 AY, since one horse-power corresponds with
33,000 foot-pounds per minute. {See also Chap. IX.)
Example 41. — If 4 amperes flow through a resistance
of 4J ohms for twenty minutes, how many foot-pounds
of work are done"? Answer. — 63,720.
Example 42. — If three-quarters of an ampere flows
through an Edison lamp when 108 volts are maintained at
its terminals, how many foot-pounds of work per minute
are expended on the lamp 1 Answer. — 3,584^.
Example 43. — A horse-power being 33,000 foot-
pounds per minute, how many such Edison lamps as are
referred to in the last question would be made to incan-
desce with the expenditure of 2 J horse-power 1
Answer. — 23.
202 PRACTICAL ELECTRICITY. [Chap. IV.
Example 44. — If a lamp through which half an ampere
is flowing, and at the terminals of which 85 volts are
maintained, emit 10 candles of light, how many candles
per horse-power are being produced %
The horse-power expended equals
44-25 X ^ X 85 .
33,000 '
therefore one candle requires an expenditure of
44-25 X A X 85 ,
^^^ A^ horse-power;
330,000 ^ '
therefore one horse-power will produce
330,000 .„ . .
-— — — — illumination.
44-25 X J X 85
Answer. — 175-5 candles' illumination nearly.
As already stated, it can be shown in all cases
that the total work done in the external circuit equals
44 "25 AY foot-pounds per minute, whether there be
electromotors or voltameters or not in this circuit. If,
however, there be either of these, the total work done
will be more than 44*25 A^r foot-pounds per minute
where r is the total resistance of the external circuit,
that is,
44-25 AY. > 44-25 A2 r.
In fact, 44*25 A^ r foot-pounds per minute represents
the portion of the energy that is turned into heat, and
the difference represents the amount of electric energy,
measured in foot-pounds per minute, that is transformed
into some form of energy other than heat.
Electromotive Force.
115. Work done by a Current Generator. Electro-
motive Force. — In order that a given amount of work may
be done on the external circuit, a greater amount of
work must be done by the generator itself, on account of
Chap. IV. I ELECTROMOTIVE FORCE. 203
the resistance of the generator against which the current
has to be sent, just as a pump has to do more work
than the energy stored up in the water. Consequently, if
b be the resistance of the generator in ohms, 44-25 A^ h
foot-pounds per minute must be expended in sending the
current through the generator itself, and, consequently,
the total work done by the generator in foot-pounds pei
minute equals
44-25 A2 (r + h).
Now if V be the potential difference, that would send
the current A amperes through h ohms,
A ^
^=?
or A^ 6 = A v.
Hence the total work done by the generator equals
44*25 A (V -f v) foot-pounds per minute.
Further, we know that when a current passes through
a voltameter, the amount of chemical action . that is pro-
duced in a given time is proportional to the current ;
indeed, it was the amount of chemical action per minute
that gave us our original definition of current strength.
And a galvanic battery is but a form of voltameter,
hence we may conclude that the amount of each of the
various chemical actions that take place in a battery in
a given time is proportional to the current, if no action
takes place when no current is passing, a condition that
is approximately fulfilled in a good galvanic battery.
Also we know that the amount of chemical action
that takes place in a given time in a battery represents
the amount of fuel burnt in that time, and therefore is
proportional to the total amount of work done by the
battery in the same time. The total work, therefore,
done by the battery per minute is proportional to A ;
but we have seen that it is also proportional to
A (V+t?), consequently, Y-\-v must be a constant for a
204 PRACTICAL ELECTRICITY. [Chap. IV.
particular battery. This constant is called the " electro-
motive force" and is shortly represented by the letters
" E. M. F" If the current passing through the battery
is very large its chemical constitution changes somewhat,
so that the same current passing through it for the same
time does not produce the same chemical decomposition
as before ; hence the work now done, compared with the
work previously done, ceases to be in the ratio of the
present value of the current to the former value, or, in
other words, V+ t^ or the E. M. F. is no longer constant.
However, excluding such extreme cases, we can say
that the current
^ = ?'
r
or A = - ;
or A =
b
E
r + 6
r
Hence V = — ^"1; E,
if E stands for the electromotive force of the battery.
116. Variation of External Resistance, Current, and
Potential Difference at the Battery Terminals. — When
r, the external resistance, is extremely great compared
with 6, and the current, as seen from the third equation
above, is very small, V, the " terminal potential difference"
is, as seen from the last equation, a maximum, and
becomes equal to E. And as long as r is fairly large
in comparison with 6, the current remains small, and V
remains nearly equal to E. When r diminishes so as to
become small compared with &, A increases rapidly, until
when r is nought A becomes a maximum, and equals
E
— V, then, is nought.
b
Chap. IV.J TERMINAL POTENTIAL DIFFERENCE.
205
The preceding is all given concisely in the following
table : —
r
V
A
Infinity.
E
0
Great compared
with b.
Very little less
than E.
SmaU.
p,aa.Y
p-\-'b^-
E
p-^b
Small compared
with b.
Small.
Great.
0.
0.
Maximum, and
E
equal to - •
The apparatus shown in Fig. 74, consisting of a
battery B, a delicate ammeter A,
a voltmeter V, and a variable re-
sistance R, enables all the preced-
ing to be tried experimentally.
First, make E, equal to in-
finity, then the reading on the
voltmeter gives E.
Secondly, make E, have any
suitable value, so that the cur-
rent can be easily read accurately p^g 74
on the ammeter; let it be A.
amperes, and the corresponding potential difference at the
terminals of the battery V volts ; then,
V = E - A 6,
where b is the battery resistance ; . :
. . 6 = : — ohms.
206 PRACTICAL ELECTRICITY. [Chap IV
The resistance of the battery can in this way be
determined without knowing r the value of R, that is,
without employing resistance coils of known value, and
this is the best method of measuring the resistance
of a current generator when the resistance is very small,
as in the case of an " accumulator.^^
Thirdly, take various values of r, and see whether the
E
current always equals amperes, and the terminal
potential difference E — A 6 volts.
As a rough analogy, the terminal potential difference
of a battery may be likened to the force exerted by a
locomotive engine in dragging the carriages, which is, of
course, equal to the pull on the coupling connecting the
engine with the first carriage, while the current strength
may be likened to the speed of the train, and the external
resistance to the mass of the carriages composing the
train. If the train be long and heavy, corresponding
with a great external resistance, the pull exerted by
the engine is great, but the speed of the train is slow.
Whereas if there be only a few carriages the pull is
less but the speed is greater, and in the extreme case,
when the engine is running alone the pull exerted on the
coupling, which is now hanging loose, is nought, and the
speed of the train is the greatest. Also the pull exerted
by the engine on the first carriage is always less than the
total force exerted by the engine, unless the engine is
attempting to pull so heavy a train that it does not move,
corresponding with infinite external resistance and cur-
rent nought, because if the engine is moving at all, some
of its pulling power is employed in moving itself. And
so with a battery, if any current at all is flowing, the
terminal potential difference must always be slightly less
than the electromotive force.
Example 45. — A Daniell's cell has an E. M. F. of 1 -07
volts, and an internal resistance of 2 J ohms; what
Chap. IV. J EXAMPLES. 207
current will it send through an external resistance of
32 ohms'? Answer. — 0'031 ampere nearly.
Example 46. — A battery having an E. M. F. of 15
volts, and an internal resistance of 25 ohms, is sending a
current through an external resistance of 5 ohms ; what
is the potential difference at the battery terminals 1
Answer. — 2 J volts.
Example 47. — What current must the battery in the
last question send so that its terminal potential difference
may be 7 "5 volts? Answer. — 0*3 ampere.
Example 48. — If a battery, having an E. M. F. of 8
volts, have its terminal potential difference reduced to
2 volts on sending a current of 2 amperes, what is its
internal resistance 1 Answer. — 3 ohms.
Example 49. — A battery has a terminal potential
difference of 15 volts when sending a current of 2
amperes, and 12 volts when sending a current of 3
amperes ; what is its internal resistance 1
If E be the unknown E. M. F. of the battery, and h
its resistance,
we have 15 = E - 26,
also 12 = E - 3 6,
or 6 = 3 ohms.
Answer. — 3 ohms.
CHAPTER V.
CURRENT GENERATORS.
117. Current Generators— 118. Batteries— 119. DanicU's Cell— 120.
Minotto's Cell — 121. Gravity Daniell — 122. Chemical Action in
the Daniell's Cell— 123. Local Action— 124. Grove's CeU— 125.
Bunsen's CeU — 126. Leclanche Cell — 127. Potash Bichromate
Cell — 128. Measuring the Electromotive Force of a Current
Generator — 129. Measuring the Resistances of Batteries-
ISO. P. D.— 131. Comparing the Electromotive Forces of Bat-
teries—132. Poggendorff's Method of comparing Electromotive
Forces — 133. Electromotive Force of a Cell is Independent of
its Size and Shape — 134. Calibrating a Galvanometer by Em-
ploying Known Resistances and a Cell of Constant E. M. F.
— 135. Ai-rangements of Cells— 136. Arrangement of a given
Number of Cells to produce the Maximum Current through a
given External Resistance— 137. Variation produced in the Total
Current by Shunting a Portion of the Circuit — 138. Constant
Total Current Shunts— 139. Independence of the Currents in
Various Circuits in Parallel.
117. Current Generators. — The current generators in
practical use may be divided into —
1. "Batteries."
2. " Accumulators " or " Secondary batteries.**
3. ** Magneto machines."
4. "Dynamos."
5. "Thermopiles.*'
All of these are simply contrivances for converting
various forms of energy into electric energy. In thermo-
piles heat energy is directly transformed into electric
energy, just as in a steam-engine heat energy is directly
transformed into mechanical energy, or energy of visible
motion. In dynamos and magneto machines there is a
direct transformation of mechanical energy into electric
energy, whereas in accumulators and batteries it is
stored up^ or potential, chemical energy that is converted
into electric energy.
Chap, v.]
BATTERIES.
209
118. Batteries. — A " hattery " is the name given to
a collection of ^^ galvanic cells, ^^ arranged so as to pro-
duce a larger current 11
than could be obtained T
with a single cell under
the particular circum-
stances. Fig. 75 shows
a battery composed of
five cells of the very
simplest form, each cell
consisting of a plate of
zinc z and a plate of
copper c, dipping into
dilute sulphuric acid.
Such a cell is frequently
called a " simple Voltaic
element." The copper
plate of one cell is joined
by means of a copper
wire to the zinc plate
of the next, so that the
cells are in series (see
Arrangements of Cells,
§ 135, page 239), and on
joining the two terminal
copper wires marked -{-
and — in the figure,
directly together, or to
the terminals of a gal-
vanometer, voltameter,
or other indicator of
the direction of the
current, the current is
found to flow in the
direction of the arrows
(see Definition of the Direction of the Current, § 7, page 1 4).
A great number of cells have been devised from time
to time, but the most important are the
o
210 PRACTICAL ELECTRICITY. [Chap, V.
1. "Daniell's" cell.
2. "Grove's" cell.
3. "Bunsen's" cell.
4. "Leclanch6" cell.
5. "Potash bichromate" cell.
Other cells, such as the ^^ Lalande Chaperon,''^ the ^''Ross,^'
the " Upward" the ^^ Regent" &c., may be used for the
Fig. 76.
comparatively cheap production of large currents, when a
dynamo is not available, but such cells cannot, as far as the
author is aware, compare with the dynamo in economy.
119. Daniell's Cell.— The ''DanieU's" cell consists
of a copper plate c. Fig. 76, dipping into a solution of
copper sulphate contained in a glass, or glazed, highly
vitrified stoneware jar, J, and a zinc plate, or rod, z, to
which a copper wire, or strip, w, is soldered, dipping into
either dilute sulphuric acid or a solution of zinc sidphafe,
the two solutions being separated by a porous partition P,
chap, v.]
DANIELL*S CFAiL. 211
made of unglazed earthenware, and called a " poroiu
fot" The E. M. F. of a Daniell's cell, and of all its
modifications, is roughly M volts, but it varies from
about 1-07 volts to 1-14 volts, depending on the densities
of the solutions of copper and zinc sulphate. With equi-
dense solutions, and with^ plates of pure zinc and copper,
the E. M. F. is 1-104 volts. This value is increased by
increasing the density of the copper sulphate solution,
and diminished by increasing the density of the zinc
sulphate solution, and is scarcely at all affected by the
ordinary atmospheric changes of temperature. {See
§ 215, page 411.)
The resistance of the cell varies with the area of the
copper and zinc plates immersed in the liquids, the dis-
tance between the plates, and the thickness and constitu-
tion of the walls of the porous cell. With a cell about
7 inches high, of the relative dimensions shown in the
above figure, the resistance may be as low as J of an
ohm when the solution in which the zinc plate is im-
mersed is dilute sulphuric acid of a specific gravity of
about ri5 at 15° C. Occasionally, however, porous pot
Daniell's cells, with smaller plates, are used, having a
resistance of as much as 10 ohms. The E. M. F. of the
Daniell, or of any other form of cell, is quite independent
of the size of the various parts of the cell, or of the cell as
a whole, and depends solely on the materials employed in
its construction. (See § 133, page 236.)
120. Minotto's Cell.— In the ''Minotto's''* cell the
porous pot is replaced by a layer of sand or sawdust,
and it is constructed as shown in Fig. 77. At the bot-
tom of a glass, or glazed and highly vitrified stoneware
jar J, there is placed a disc of sheet copper c, to which is
attached one end of an insulated copper wire, which
passes up through the cell. Above this plate are placed
some crystals of copper sulphate c s, and on the top a
piece of thin canvas c, separating the copper sulphate from
the layer of sand or sawdust s, and on the top of the savr-
* Often wrongly spelt *' Menotti^s."
212
PRACTICAL ELECTRICITY.
[Chap. V.
dust rests the zinc plate z, separated from the sand or saw-
dust by a piece of thin canvas c. The cell is completed by
pouring in some solution of zinc sulphate, so as to cover
the zinc disc, but not so much as to reach up to the brass
binding screw b, cast into the top of a little column of
zinc, forming part of the zinc disc. Before putting
in the sand or sawdust,
it should be soaked in a
solution of zinc sulphate,
and squeezed partially
dry, because, if put into
the cell quite dry, a long
time must elapse before
the liquid will soak
through the sand or saw-
dust, and until this hap-
pens the cell will not
come into action.
It is better to employ
sand in stationary Min-
otto's cells, as it sinks
down as the copper
sulphate is consumed, but
if the cells have to be
moved about, then it is batter to use sawdust.
121. Gravity Daniell. — In some types of Daniell's
cells, no form of porous partition is employed, and the
copper sulphate and zinc sulphate are kept separated solely
by the action of gravity, the zinc sulphate solution being
put at the top, as it is the lighter of the two. Such cells
are called " gravity DanieWs,'^ and examples of them are
shown in Figs. 78, 79, and 80. Fig. 78 shows two forms
of the " Meidinger " cell, in each of which the copper plate
is put inside a small inner glass tumbler d d, so that the
particles of zinc sulphate^ which may become detached
from the zinc plate, may fall clear of the copper plate,
and be prevented from coming into contact with it.
In the type of Meidinger shown on the left, the crystals
Fig. 77.
Chap, v.]
GRAVITY DANIELL.
213
of copper sulphate are in a glass tube h, with only a
small hole at the bottom, while in the type to the right
the crystals are contained in an inverted flask open
at the neck. In both, the zinc plate z z, which is in
the form of a cylinder, is supported on a shoulder h b,
formed by a contraction of the lower part of the outer
glass vessel. The Ccdlaud cell, Fig. 79, is a simplifica-
tion of the Meidinger, being without the reservoir for
Fig. 78.
the copper sulphate crystals, and the small glass tumbler
to hold the copper plate.
In the ^^ Lockwood^^ cell. Fig. 80, the zinc plate is
made like a kind of wheel with spokes, so as to expose a
large surface to the liquid, and is supported by three
lugs resting on the edge of the glass vessel. The
copper plate is made of thick copper wire, bent into
the form of a double spiral, with the crystals of copper
sulphate placed between the spirals, the upper spiral
214
PRACTICAL ELECTRICITY.
[Chap. V.
being found to retard the travelling up of the copper
sulphate solution to the zinc plate if the cell be kept
sending even only a weak current. For the lower spiral,
a copper disc, similar to that used with the Minotto's
cell (§ 120, page 211), may be substituted, and for the
upper one, a perforated copper disc, without interfering
with the action of the Lock wood cell. All gravity cells
have the disadvantage that they cannot be moved about,
Fig. 79.
Fig. 80.
otherwise the liquids mix, and the sulphate of copper
solution coming into contact with the zinc plate, deposits
copper on it. This impairs the action of the cell by
causing the zinc plate to act electrically like a copper one.
Indeed, without any shaking, the liquids mix by diffu-
sion, even when a porous pot is employed, and hence a
DanielFs cell is found to keep in better order if it be
always allowed to send a weak current when not in
use, since the current uses up the copper sulphate solu-
tion instead of allowing it to diffuse.
A^)
'W^
Chap, v.] CHEMICAL ACTION IN THE DANIELL's CELL. 215
122. Chemical Action in the Daniell's Cell— The
DanielVs cell, and all its modifications^ produce a cur-
rent hy the formation of zinc sulphate, and the using up
of copper sulphate, the zinc plate being eaten up to form
the zinc sulphate, and the copper plate growing hy the
deposit of metallic copper on it. Chemically, the action
may be represented as follows — the " water of crystalli-
sation " of the copper and zinc sulphate crystals, as well
as the water employed to form the solutions, being
omitted for the sake of simplicity :^-
g
Before sending a current V
k{CM)-{-l{CnSO^) I »«(ZnS04)+«(Zn),
after sending a current §
(^-+l)(Cu)+(^l)(CuS04) g (m+l)(ZnS04) + («-l){Zn);
o
Ph
k and n being any arbitrary quantities of copper and
zinc used in the copper and zinc plate, and I and m any
arbitrary quantities of the copper sulphate and zinc sul-
phate employed. Substituting the " atomic weights " for
the various substances employed, we find that for every
26 ounces of zinc that are dissolved off the zinc plate, about
100 ounces of copper sulphate crystals are decomposed, and
about 25 ounces of copper added to the copper plate. If
dilute sulphuric acid be employed in place of a solution
of zinc sulphate, the resistance of the cell is lower, and the
E. M. F. higher, but the latter is not so constant as when
zinc sulphate alone is used, because, if we start with dilute
sulphuric acid, zinc sulphate will be gradually formed
by the action of the cell, and the increase of the amount
of zinc sulphate we have already seen lowers the E. M. F.
The chemical action in that case will be as follows : —
a
Before sending the current -J
A(Cu)+?(CuS04) I m(H2S0^)-\-n{Zn),
after sending the current g
(A:+l)Cu+(M)(CuS04) 2 m(H2S04) + (ZnS04) + («-l)(Zn)
o
PL4
216 PRACTICAL ELECTRICITY. [Chap. 7
WheUj therefore^ constancy of E. M. F. is desired, a
solution of zinc sulphate should be used, and not dilute
sulphuric acid.
If the copper sulphate solution becomes too weak, the
water is decomposed instead of the copper sulphate, and
hydrogen is deposited on the copper plate. This deposition
of hydrogen lowers the E. M. F., and care should therefore
be taken to keep up a sufficient supply of crystals of copper
sulphate. Indeed, it was for the purpose of preventing
the deposition of hydrogen on the copper plate which
occurs with a simple voltaic element, that Prof. Daniell
was led to use copper sulphate as a " depolariser," and
thus invent the " two-fluid cell." This polarisation is
easily seen by dipping two pieces of clean copper, C^ and
Cg, and a piece of zinc, into dilute sulphuric acid, a part
of each of the three pieces being inside the liquid and a
part outside, but the three pieces not touching one
another, either inside or outside the liquid. If the two
pieces of copper, C^ and Og, be first joined by wires with
a delicate galvanometer, no current, will be observed ; but
if one of them, Cj, be connected for a time with the zinc
by a wire, so that a current flows from 0^ to the zinc
through this wire, and from the zinc to C^ through the
liquid, it will be found on stopping this current and con-
necting Cj and O2 again with the galvanometer, that a
current now flows round it from Cg to 0^, that is, from
Cj to Cg through the liquid. Using 0^, therefore, as the
copper plate in a simple voltaic element, causes it to act
subsequently as a zinc plate to a clean copper plate.
And the longer Cj is used as the copper plate of the
simple voltaic cell, which is sending a current through
a piece of wire to the zinc plate, the more like a zinc
plate does C^ become, and the weaker grows the cur-
rent that Oj with the zinc plate can send through a
given external resistance, while the stronger becomes
the current that Cj and a clean piece of copper will
send through a given resistance. This change in the
behaviour of Cj is due to a deposition of hydrogen on
Chap. V.l LOCAL ACTION. 217
it, which deposition gradually disappears when C^ and
Cg are left connected. Both then when the ^^ 'primary
current''^ flows from the zinc to C^ through the liquid,
and subsequently when the " secondary current " flows
from Cj to Cg also through the liquid, the hydrogen
moves in the direction of the current, the result
obtained with a sulphuric acid voltameter {see § 7,
page 15).
If the solution of zinc sulphate in a Daniell's cell
(Figs. 77, 80) becomes too strong by the evaporation of the
water, the zinc sulphate crystallises on the sides of the cell,
and the liquid passes up by capillary attraction between
the film of crystals and the side of the vessel, crystallising
again above. At last the film passes over the edge of the
jar and forms on the outside, thus making a kind of
syphon, which draws off the liquid. This action may, to
a great extent, be prevented by warming the edges of the
glass or stoneware jars, and of the porous pots, before the
cells are made up, and dipping them while warm into some
paraffin wax melted in warm oil. It is desirable also with
those Daniell's cells in which the zinc is inside the porous
pot, as in Fig. 76, to dip the bottom of the porous pot into
the melted paraffin wax, otherwise particles of metallic
copper will be gradually deposited in the pores at the
bottom of the porous pot on which the zinc rests, and
the cell will become " short-circuited,''^ that is, a strong
current will be sent through this copper, and the mate-
rial in the cell will be used up rapidly, exactly as would
be the case if the zinc and copper plates were perma-
nently connected by a short piece of thick copper wire
outside the cell.
123. Local Action. — Another cause of ^^ local action"
or the production of useless currents, is impurities, such
as bits of coke, in the zinc. If a piece of coke and
a piece of pure zinc be put into dilute sulphuric acid,
then, as long as the coke and zinc do not touch one
another, either in the liquid, or outside, no appreciable
chemical action will take place ; but if now the parts of
2l8
PRACTICAL ELECTRICITY.
[Chap. V.
the coke and zinc that are in the liquid, or the parts
that are outside, be touched together, a rapid evolution
of hydrogen gas will take place, together with the forma-
tion of zinc sulphate. And exactly the same effect is
produced when a piece of zinc containing impurities is
dipped into dilate acid. This local action, however,
can be prevented by coating the surface of the zinc
with an " amalgam " of zinc and mercury, or " amalga-
mating " the zinc, as it is shortly called, this amalgam
covering up the impurities. To
amalgamate a piece of zinc, it
should be dipped into dilute
sulphuric acid, to clean the
surface, when a little mercury
should be rubbed over the zinc
with a piece of rag tied to a
stick. A plate of commercial
zinc amalgamated, although
much cheaper than a plate of
pure zinc, does not give an
E. M. F, as constant as is ob-
tained with a pure zinc plate.
g, 124. Grove's Cell.— In the
W "Grove's^' cell the copper plate
intheDaniell's cell is replaced by
a sheet of ^:>Z<x^^n^tm, p, Fig. 81,
and the solution of copper sul-
phate by strong nitric acid. Dilute sulphuric acid, in the
proportion of about one pint of acid to ten pints of
water, is used in place of zinc sulphate solution, since, with
the Grove's cell, we wish to obtain the highest E. M. F.,
and the lowest resistance rather than very great con-
stancy. The E. M. F. is about 1-93 volts, and with good
porous cells the resistance is very low, being only about
3-6 X 6? ,
ohms.
Fig. 81.
where d is the distance, in inches, between the platinum
Chap, V.I grove's CELL. 219
and the zinc plates, and A the area, in square inches, of
the platinum plate immersed in the nitric acid. If, as is
frequently the case, the zinc plate z z is cast in the shape
shown in Fig. 81, A must be reckoned on both sides
of the platinum plate p. When the cell has the dimen-
sions indicated in the figure, the resistance is about 0*15
ohms when the nitric acid is strong, and the dilute sul-
phuric acid has but little zinc sulphate in it. After a
Grove's cell has been sending a current for some time, the
nitric acid becomes weakened, as water is formed by the
action of the cell, and a considerable quantity of zinc
sulphate is also dissolved in the dilute sulphuric acid,
both of which have the effect of diminishing the E. M. F.,
and increasing the resistance of the cell.
The chemical action is as follows : —
g
Before sending a current :3
*(Pt)-}-/(HN03) I w(HoS04)-|-w(Zn),
after sending a current ^
A(Pt) + (^-2)(HN03) « {m-l){lISO,) + {ZnSO,)
+ (NA)+2{H20) o -t-(«-l)(Zn) ;
o
(k
the water originally in the cell being omitted for simpli-
fication. Peroxide of nitrogen, NgO^, comes off" as a
dark brown gas, extremely unpleasant and unhealthy
when breathed for any time ; a Grove's battery should,
therefore, always be placed either in the open air or
under a chimney when in use.
The large E. M. F., combined with the small resist-
ance, makes Grove's cells very valuable when a very strong
current has to be produced ; hence, before the perfection
of the dynamo and of secondary batteries, they were
largely used for the production of the electric light.
125. Bunsen's Cell.— The « Bunsen's " cell differs from
the Grove's only in having a cylinder, or block, of carbon
in place of the sheet of platinum, as seen in Fig. 82,
which shows a common form of circular Bunsen's cell,
C being the carbon, and Zn the zinc. A Bunsen's cell is
220
PRACTICAL ELECTRICIT7.
[Chap. V.
cheaper to construct than a Grove's cell, as carbon is so
much less expensive than platinum ; it is, however, more
cumbersome, and more nitric acid is required to fill it, as
the nitric acid soaks into the pores of the carbon. The
E. M. F. of a Bunsen's cell is also somewhat lower than
that of a Grove's, although the chemical action in the
two cells is nearly the same.
The carbons for the Bunsen's cells are either cut out
Fig. 82.
of retort carbon, or are made by baking in a furnace fine
coke-dust and caking coal in an iron mould ; then, in
accordance with a process invented by Bunsen, the baked
mass is soaked repeatedly in thick syrup or gas-tar, and
re-baked to impart solidity and conducting power to it.
126. Leclanch6 Cell.— The ^^ LeclancW cell consists,
as seen in Fig. 83, of a zinc rod to the left of the figure,
immersed in a solution of ordinary sal ammoniac, and a
plate of carbon put inside a porous pot, and packed
tightly with a mixture of the needle form of manganese
peroxide and broken gas-carbon. Both the mauganese
Cliap. V.J
LECLANCHE CELL.
221
peroxide and the gas-carbon must be sifted to remove the
dust, in order that as much surface as possible may be
exposed to the action of the liquid. The porous pot is
merely for the purpose of holding the mixture in posi-
tion, and not for keeping two liquids separated, as in the
cells previously described ; for, in fact, there is only one
liquid on both sides of the
porous pot — the solution of sal
ammoniac. The upper part of
the porous pot is closed with
pitch, in which a small hole is
left, so that a little water or a
little solution of sal ammoniac
may be poured in to start the
action.
The chemical action is as
follows : —
Before sending a current
^•C+/(Mn02) + w(NH4Cl) -i-w(Zn),
after sending a current
kC+{l-2)(Mn02) + (w-2) (NH4CI)
+ (Mn^Oa) + 2(NH3) + (H.0) +
(ZnCl2) + («-l)(Zn).
Ammonia, NH3, therefore,
comes off from the cell, and Fig. 83.
substituting the atomic weight
we see that for every 50 grains of zinc used up about 82
grains of sal ammoniac are consumed, and about 134 grains
of manganese peroxide, MnOg, are reduced to the lower,
or sesqui-oxide, MnoOg. If too little sal ammoniac be pre-
sent, zinc oxide is formed instead of zinc chloride, and
the solution becomes milky. When this happens, more
sal ammoniac should be added. Connection with the
carbon rod is made by means of a lead cap cast on it ;
and to prevent a salt of lead being formed between the
cap and the carbon, which would introduce a high resist-
ance, the end of the carbon rod is heated for an hour in
paraffin wax, at a temperature of 110° C, before the cap
222 PRACTICAL ELECTRICITY. [Chap. V
is cast on, then two quarter-inch holes are drilled side-
ways through the carbon, and the cap cast on, the lead
which runs into these holes serving as rivets.
The E. M. F. of a Leclanche cell is 1-47 volts, but
it falls rapidly when the cell is used to send a strong
current. It will, however, regain its value if the cell be
left for some time unused, and it does not sensibly
diminish when the cell is put on one side, even for some
months. Hence, while the Leclanche cell is much in-
ferior to the DanielVs for the purpose of sending a steady
current for an hour or two, it is much superior to the
Daniell for the sendi7ig of intermittent currents at any
time during the course of many months— for example,
such currents as are employed for the ringing of electric
bells.
127. Potash Bichromate Cell. — These cells are some-
times made without a porous cell, as seen in Fig. 84, and
sometimes with, as seen in Fig. 85. The plates employed
are of carbon and zinc, and in Fig. 84 the two outer
plates are of carbon, and dip continuously into the liquid,
while the middle plate is of zinc, and is only pushed
down, by means of the handle a, into the liquid when
it is desired that the cell shall send a current, and with-
drawn as soon as the current is inteiTupted. The follow-
ing is the best composition to give to the liquid : —
Potash bichromate ... lib.
Strong sulphuric acid 2 lbs.
Water ... 12 lbs.
or, as it is inconvenient to weigh the sulphuric acid and
the water, ten pints of the same composition may be
made as follows : — Add with constant stirring to 0*832
pints of sulphuric acid, having a specific gravity of about
1'836, 0-955 lbs. of pulverised commercial potash bichro-
mate, KgCrgOy ; and when the formation of the chromic
acid, CrOg, and potash sulphate, KoSO^, produced by
the mixture, is completed, pour in slowly 9 -2 pints of
cold water. The liquid will become gradually warm,
and the crystalline precipitate be entirely dissolved.
Chap. V.J
POTASH BICHROMATE CELL.
223
The chemical action produced by this mixing may be
represented as follows : —
KaCr^Oy + THaSO^ = 2Cr03 + K^SO^ + HgO
and the chemical action that takes place in the cell dur-
ing the passage of the current consists in the formation
^l||J,#^
Fig. 84.
Fig. 85.
of chromium sulphate, Cro3(S04) ; zinc sulphate, ZnSO^ ;
and water, HgO, and may be represented thus : —
SCrOg 4- 6H2SO4 + 3Zn = Cro3(S04) + SZnSO^
+ 6H2O.
This cell gives rise to no disagreeable fumes, has a
high E. M. F. of something like two volts, and a low in-
ternal resistance. The E. M. F., however, rapidly falls
when the cell is employed to send a strong current con-
tinuously, but recovers its original value when the cell
has remained out of action for some time.
With the type of potash bichromate cell, having a
porous pot, the zinc z (Fig. 85) is frequently cast, in the
224 PRACTICAL ELECTRICITY. [Chap. V.
form of a block, on to a stout copper wire, carrying the
binding screw, and both the block and the wire are well
amalgamated. In the porous pot containing the zinc,
there is put a small quantity of mercury to maintain the
amalgamation, and either dilute sulphuric acid, in which
case the chemical action is the same as in the cell with-
out the porous pot, or, instead, a solution of common
salt, NaOl, when zinc chloride, ZnClg, is formed instead
of zinc sulphate, and sodium sulphate, NagSO^ in addi-
tion to the chromium sulphate. The complete chemical
action is in this latter case : —
Before sending the current -g
A;C+ZCr03-l-3/H2S04 f^ mNaCl+wZn,
After sending the current g
kG + (^2) 003+ I {m-&) NaCl + 3Na2S04 +
3(^2)H2S04-|-Cr23(SOj ^ 3ZnCl2+6H20-j-(w-3).Zn.
When the supply of potash bichromate becomes ex-
hausted, the orange colour of the solution turns blue, and
when this change of colour is observed, more potash
bichromate should be added. If, however, the cell be-
gins to fail when the orange colour still remains, then
more sulphuric acid is needed.
As no other form of current generator than galvanic
cells need be employed for any of the experiments that
precede this, or, indeed, for many that follow, the descrip-
tion of dynamos, thermopiles, &c., will be deferred.
128. Measuring the Electromotive Force of a
Current Generator. -— An electrometer, or voltmeter,
measures the potential difference at its terminals, and,
as shown in § 116, page 204, the potential difference at
the terminals of a generator of constant E. M. F. is equal
to its E. M. F. when no current is flowing, and practically
differs but very little from its E. M. F. when but an
extremely small current is flowing. Hence, to measure
the E. M. F. of a generator of constant E. M. F., we must
arrange that either it shall send no current at all, or, at
any rate, but a very small one. The first condition
can be fulfilled when an electrometer is employed, and
Chap, v.] MEASURING THE RESISTANCES OF BATTERIES. 225
the second even with a voltmeter if it has a very large
resistance. In order to ascertain how large this resist-
ance may be, we must consider the equation
r + 0
and from that we see that in order that V may be
practically equal to E it is necessary that r and b should
be practically equal to r; that is, r must be large compared
with b, and hence the battery must be sending a very
small current through the voltmeter, compared with what
it could produce if its terminals were joined with a short
bit of thick wire. (See § 131, page 231, and following sec-
tions, for further details about measurement of E.M.Fs.)
129. Measuring the Resistances of Batteries. —
We have already seen, in § 116, page 205, one way of
determining the resistance of a battery without the aid
of a resistance box, by making simultaneous measure-
ments with an ammeter and voltmeter. This method is
particularly suitable to be employed with current gene-
rators of very low resistance, such as accumulators, since
such generators would send a very powerful current
through any coil having a resistance comparable with
their own, and this current would tend to heat such a
coil, and alter its resistance, unless it were made of very
thick wire. Hence, it would be very difficult to employ,
with such a generator, resistance coils having perfectly
constant and known resistances, unless their value, com-
pared with the resistance of the generator, was so high
that the slightest proportional error in the value of the
coils would make a serious error in the determina-
tion of the resistance of the generator, just as a large
error would probably be introduced if an attempt were
made to weigh a few grains of some powder in a weigh-
ing machine suitable for weighing a hundredweight.
Beginners are apt too frequently to forget thai;, although
a coil of 10,000 ohms, and another of Tooth of an ohm,
may be put in boxes of about the same size, there is the
p
226 PRACTICAL ELECTRICITY-. fChap. V.
same sort of difference between these resistances as be-
tween twelve pounds and one grain, or between thirty
tons and one ounce, and hence that apparatus which is
arranged to measure the one is totally unsuited to
measure the other.
With current generators of constant E. M. F., and
having higher resistances, the following methods, with
which resistance coils of known value are employed,
may be used.
1st. Let C and C, as determined from the deflections
on a galvanometer and reference to the relative calibra-
tion curve, be the relative strengths of the currents pro-
duced by the generator when resistances r and r' in
ohms are introduced in the circuit ; then, if h be the
resistance in ohms of the generator, g that of the galva-
nometer, and E the E. M. F. in volts — which latter need
not, however, be known —
E EC
^^ b + r^g^G^
b + r +g C '
. ^^C-(/ + ^)-C(r4-V)
C-C
If r and r' be so chosen that 0 is twice C, then
b = r' — 2r—g.
2nd. Let C and C be the relative strengths of the
«;urrents produced : first, when the galvanometer is un-
shunted, and a resistance r ohms introduced in the main
circuit ; secondly, when the galvanometer of resistance g
ohms is shunted with a shunt of s ohms, and when a re-
sistance r' ohms is in the main circuit, then
E ^ _s_ E _ G
h+r-\-g 8-hg ^^^'^^l_ ~ ^'*
s+9
Ch(ip. v.] MEASURING THE RESISTANCES OF BATTERIES. 227
C'{s+g)-C8.
If s and 7*' be so selected by trial that C equals 0,
then we have
The objection to both these methods is that on ac-
count of the variation in the current strength, and on
account of the time that each of the two currents C and
C has to be allowed to flow until the deflection of the
galvanouieter needle becomes steady in each case, the
E. M. F. and resistance in some types of cells is liable to
undergo a change from polarisation. On this account
the " condenser method of measuring the resistance oj
current generators'^ described in § 184, page 342, is to be
preferred.
Example 50. — A DanielFs battery produces a deflec-
tion of 38° on a tangent galvanometer when a resistance
of 27 ohms is inserted in the circuit, and a deflection of
46° when this resistance is reduced to 12 ohms. What
is the resistance of the battery if that of the galvanometer
be 2i ohms 1
Inserting these values in the equation, we have
_ tan. 38° X (27 + 21)- tan. 46°x (12 + 2|)
~ tan. 46° -tan. 38°.
Answer. — 31^ ohms about.
Example 51. — With a galvanometer having a resist-
ance of half an ohm, and constructed so that the angular
deflection is directly proportional to the curre«it, a bat-
tery of 20 Grove's cells in series produces a deflection of
28 divisions when a resistance of two ohms is inserted,
and 14 divisions when a resistance of eight ohms is in-
serted. What is the resistance of the battery 1
228 PRACTICAL ELECTRICITY. [Chap. V.
If b be the resistance of the entire battery,
6 = 8-2x2-1
Answer. — SJ ohms.
Example 52. — When four ohms are introduced into
the circuit of a sine galvanometer, having 6 ohms' re-
sistance, and a Leclanche cell, a deflection is produced
corresponding with a necessary rotation of the sine gal-
vanometer through 22°. When, however, the sine galva-
nometer is shunted with two ohms, the rotation required
is only 8°. What is the resistance of the Leclanche cell ?
Substituting the values in the equation, we have
h - ^^' ^^° X (4 + 6) X 2 -sin. 8° X {(2 + 6) X 4 + 2 X 6}
sin. 8° X (2 + 6) - sin. 22° x 2
Answer. — 4 ohms about.
Example 53. — The same deflection is produced on a
galvanometer of 2\ ohms' resistance, when 8 ohms are in
circuit, as when only 2 ohms are in circuit, and the gal-
vanometer is shunted with 2 ohms. What is the resist-
ance of the current generator 1
j^ 2x(8-2)-2|-x2
Answer. — 2^ of an ohm.
In making measurements of the resistance of lot-
teries by any of the foregoing methods, care must be taken
not to introduce into the circuit resistances that are very
large compared with the resistance of the battery which
we desire to find, since any error in such a high resistance
will probably introduce a large error into the answer. Por
example, suppose it be desired to use a galvanometer
which happens to be so delicate that on attaching the
battery directly to its terminals, so large a deflection is
produced that it requires a considerable resistance to be
introduced into the circuit to reduce this deflection to
readable limits, then it would be better to reduce the prac-
tical sensibility in some other way than by adding resistance
Chap, v.] MEASURING THE RESISTANCES OF BATTERIES. 229
in the main circuit. This may be done either by putting
a magnet near the galvanometer or by shunting it. In
the latter case the shunted galvanometer would take the
place of the simple galvanometer in the first method
given above for determining the resistance of a battery,
and of the unshunted galvanometer in the second method ;
the second experiments referred to in the second method
being performed with the galvanometer shunted with a
different shunt.
For example, suppose we desire to determine the re-
sistance of a battery that we know to be about one ohm,
and the only galvanometer available is a very delicate one,
having 1,000 ohms' resistance, how should we proceed?
The deflection can be reduced to readable limits either by
inserting a large resistance into the circuit, or by putting
a magnet near the galvanometer, or by shunting it. As
the resistance of the galvanometer is 1,000 ohms, which
is large compared with that of the battery, introducing
another large resistance into the circuit for the purpose
of diminishing the deflection would only increase the
probable error due to the large resistance in the circuit.
Putting a magnet near the galvanometer would be better
than this, but a still better method would be to shunt
the galvanometer, because, if it be very sensitive, a suit-
able deflection may be obtained with a shunt perhaps of
one or two ohms, and with one or two ohms in the main
circuit. Suppose with a shunt of two ohms, and a re-
sistance of three ohms in the main circuit, a deflection
extending over about half the scale is obtained, then this
arrangement can be well used, either for the first or for
the second method of measuring the battery resistance.
For carrying out the first method, we may make two tests,
the first with the three ohms, and the second with,, say,
one-and-a-half ohms in the main circuit, the galvano-
meter being shunted in each case with the two ohms, and
having, therefore, a combined resistance with the shunt of
- — Yru^ ohms. For carrying out the second method we
2 -|- 1000
230 PRACTICAL ELECTRICITY. fCliap. V
might make the same first test as before, but the second
might be made with an interposed resistance of perhaps
one-and-a-half ohms in the main circuit, and with the
galvanometer shunted with, say, one ohm instead of the
two ohms previously employed.
To ascertain what is the formula to be employed
in this case, let r and r' be, as before, the resistances put
into the main circuit in the two tests, and s and s' the two
shunts employed, then
8 E . s E 0
or £ . {s'-{-g)(b + r')-\-s'g ^ Q
s' {s + g){b+r)-\-sg C*
. ^ ^ (^s'{{s+g)r + sg}-C's{(s'-\-gy-^s'g} .
G's{s'-hg)-Gs'(s+g)
If the battery be one that does not polarise quickly,
that is, be one in which the E. M. F. does not fall rapidly
when the battery sends strong currents, then the best way of
carrying out the first method of measuring the resistance
of the current generator with a delicate galvanometer, is
to put no resistance r in the main circuit, but to shunt the
galvanometer with a shunt that has a very small resist-
ance compared with the battery, and yet is not so small
but that a suitable deflection may be obtained. Now intro-
duce such a resistance r' into the circuit that the current
through the galvanometer becomes halved, then this re-
sistance is necessarily equal to b, since b was practically
the whole of the resistance in the circuit before the intro-
duction of r'.
130. P. D. — Throughout the remainder of this book
the letters " P. D." will be used to stand for potential
difference, in the same way as the letters E. M. F. are
universally now employed to stand for electromotive
Chap, v.] COMPARING ELECTROMOTIVE FORCES. 231
force. As these letters P. D. are here proposed as a
new abbreviation, the ordinary cumbersome expression,
"difference of potentials," has been used up to this point in
the book, in order to familiarise the reader with the mean-
ing of an expression that he will frequently meet with.
131. Comparing the Electromotive Forces of
Batteries. — The relative electromotive forces E and E'
of the batteries, or other current generators of constant
E. M. F., can be compared by observing the resistance
through which they will send equal currents. Let
h and h' be the resistances of the batteries themselves,
and r and r' the resistances, including in each case that
of the galvanometer, which, added to the resistances
b and h' respectively, cause the currents in the two cases
to be equal, then
E _ E^
E _5 + y
E' ~6'+r'*
If the galvanometer is sensitive, so that r and r',
which each include the resistance of the galvanometer,
are large compared with h and h' respectively, then
E r . ,
— = — approximately.
E r
The preceding method of comparing E. M. Fs. has
the advantage that the law of the galvanometer need not
he known.
If the currents be not the same, let C and C be the
relative current strengths obtained from the deflection of
the galvanometer and reference to the calibration curve,
then
E E^ _ 0
6 + r * 6' -f r' ~ C '
E _ 6 + r 0
®'' E'"" 6'-f / * 0'*
232 PRACTICAL ELECTRICITY. [Chap. V.
And, as before, when r and r are large compared with h
and V respectively,
E r G . , ,
— = __ . _ approximately.
E' t' C
Another method for determining the ratio of E to E'
consists in first joining the batteries up together so that
they assist one another in sending a current, and secondly
in joining them up so as to oppose one another's action.
Let C and C be the relative strength of the currents in
the two cases ascertained from the deflection of the
galvanometer and the relative calibration curve, then if
p be the total resistance in circuit in the two cases, we
have, since ^ remains constant,
E + E'
or
E' 0 - 0'
This method has the advantage that the resistances
of neither of the hatte^^ies nor of the galvanometer need
he known ; but it has the disadvantage that the sending
of currents in opposite directions through the battery
which has the smaller electromotive force is very likely
to alter this electromotive force during the experiment.
Example 54. — Two batteries having internal resist-
ances of 10 and 15 ohms produce the same deflection
on a galvanometer of 40 ohms, when 250 and 305 ohms
are respectively introduced into the circuit. What is
the ratio of their E. M. Fs. 1
Substituting the values in the equation, we have
E _ 10 + 40 + 250
' E'~ 15 + 40 + 305*
.•. E'= 1-2 K
E - E'
0
P
- Q'
E + E'
0
E - E'
-c'
E
C + (
Chap, v.] EXAMPLES. ' 233
Example 55. — The same two batteries produce the same
deflection on a much more delicate galvanometer, having
120 ohms' resistance, when 5,000 and 6,031 ohms are re-
spectively introduced into the circuit. What is the ratio
of their E. M. Fs. ?
Using the complete formula, we have
E _ 10 + 120 + 5000
E'~15 + 120 + 6031*
or E' = 1*2 E as before.
Using the approximate formula,
E _5000
E' " 6031 '
or E' = 1-206 E,
from which we see the error made by omitting the re-
sistances of the batteries and of the galvanometer in the
calculation.
Example 56. — A magneto-electric machine running at
a certain speed, and having a resistance of two ohms,
produces on a tangent galvanometer a deflection of 30°
when a resistance of 2,100 ohms is introduced in circuit
with it and the galvanometer, which has three ohms' re-
sistance. A Dani ell's cell, on the other hand, having an
E. M. F. of 1-07 volts, and one-and-a-half ohms' resistance,
produces a deflection of 45° when 84 ohms is introduced
in the circuit. What is the E. M. F. of the magneto
machine %
If E be the E. M. F. of the machine,
_1^
E = 1 -07 ^ — — - — — - X --— volts approximately.
3 + 1-5-H84 I ^y' ^
Answer. — 14-7 volts approximately.
Example 57. — What about is the E. M. F. of a
Grove's cell^ if, when joined so as to assist a Daniell's
234 PRACTICAL ELECTRICITY. [Clifip. V.
cell having an E. M. F. of 1*1 volts, a rotation of 38°
of a sine galvanometer is necessary to be made to bring
the needle to the fixed mark, whereas, when the Grove's
cell is reversed, a rotation of about 8J° in the opposite
direction is necessary] Ansioer. — 1'83 volts,
132. Poggendorfif's Method of Comparing Electro-
motive Forces. — With many types of cells the electro-
motive force is fairly constant, even for wide Variations in
the current passing through the cells, and in such a case
any of the previous methods can be employed for com-
paring their electromotive forces. But with other types,
a very small current passing through the cell is sufficient
Fig. 86.
to diminish the electromotive force. In such a case
the following method, due originally to Poggendorff, may
be employed. From what has preceded we know that
if a current of A amperes flow along a wire, J k, the
potential difference, or, shortly, the P. D., in volts between
any two points, l m, is equal to the product of A into the
resistance r of the wire, in ohms, between the points L
and M. Hence if l and m (Fig. 86) be joined by another
circuit containing a cell or iDattery of E. M. F. equal to E
and a galvanoscope, G, and if one or both of the ends of
this second circuit be moved along the wire J k composing
the first circuit until no current passes through the gal-
vanoscope G, then we know that E is equal and opposite
to the P. D. between l and m, or
E = A r.
If, now, a second battery of E. M. F. equal to E', and a
second galvanoscope, g', be attached to two other points.
Chap. V.l POGGENDORFF's METHOD. 235
u V, of the wire J k (Fig. 87)^ the points u and v being
so selected by trial that no current passes through this
galvanoscope, and if r' be the resistance of the wire u v,
then
E' = A/,
E _ r .
* E' ~ r' '
and hence the two E. M. Fs. can be compared without our
knowing the value of the current flowing through the
wire J K. If the generator is of such a nature as to
produce a constant current through the wire J K, then
Pig. 87.
there is no occasion to use two galvanoscopes, as the
points L and m can be first ascertained with the first cell,
and then the points u v with the second, such that in
each case no current passes through the galvanoscope.
If, however, the current in j k is liable to fluctuate,
then, since the essence of the test depends on the same
currents flowing from l to m as from u to v, it is better
to use two galvanoscopes, and make the two tests of no
currents through the galvanoscopes simultaneously.
Of course, care must be taken to attach the cells
or batteries whose E. M. F. we desire to compare, in such
a way that their E. M. Fs. tend to oppose the potential
differences between l and m and between u and v respec-
tively, since, if either of the cells or batteries be attached
in the opposite way, no two points, L and m or u and v,
can, of course, be found such that the current passing
through the galvanoscope attached to them is nought.
If the wire J k is everywhere uniform in material.
236 PRACTICAL ELECTRICITY. fChap. V.
section, and temperature, the resistances r and r' are
simply proportioned to the lengths l m and u v, so that
the E. M. Fs. of the batteries are simply proportioned to
the lengths of l m and u v.
The great advantage of Poggendorff's method of com-
paring E. M. Fs. is thai the com,parison is made when neither
of the batteries is sending a current; hence the same result
is obtained as if the comparison had been made with
an electrometer, and the resistances of the cells under
comparison need not be known. And, further, the sen-
sibility of the test may be far greater than could be ob-
tained with any electrometer, since the method is a
" null " method, that is, we aim at obtaining a deflection
nought, instead of measuring the deflections corresponding
with the currents produced by the batteries; conse-
quently the galvanoscope may be made as sensitive as
we please.
If the galvanometers G and G' be both sensitive, the
accuracy of the method will be the greater the longer
are the wires l m and u v, because any given small error
in the position of one of the sliders corresponding with
say a millimetre in the length of the wire, will represent
a less proportional error in the length, and so r and r can
the more accurately be compared. Hence it is desirable
to make the wire J K as long as possible, and to send
through it a steady current, so weak that the P. D., at
its extreme ends, is just equal to the larger of the two
E. M. Fs. to be compared. {See § 215, page 413.)
133. Electromotive Force of a Cell is Independent
of its Size and Shape.— The Daniell's cell (Fig. 88) is
so arranged that the copper plate c, which dips into a
solution of copper sulphate, may be made to approach,
or recede from, the zinc plate z, which dips into a solution
of zinc sulphate contained in a porous cell. By turning
the screw P, the slider, carrying the wire supporting c,
can be clamped in any position, and electric connection
can be made with the binding screws b b. Experiments
made with this cell show that, although the resistance of
Chap. V.J E. M. F. INDEPENDENT OP SIZE OF CELL.
237
the cell is varied by moving the copper plate, the E. M. F.
remains exactly the same. Further, if the screws s s be
Pig. 88.
loosened, and the copper and zinc plates be raised up as
shown in the lower figure, so that only the little projec-
tions at tJie bottom of these plates are in contact with the
238 PRACTICAL ELECTRICITY. [Cliap. V.
liquids, the E. M. F. is still unaltered. This experiment
may be quickly made by using Poggendorft's method to
compare the E. M. F. of the cell with movable plates
with that of a Daniell's cell with fixed plates, since,
as already explained, Poggendorft's method is indepen-
dent of the resistance of the cells compared. The con-
denser method of comparing E. M. Fs., described in § 183,
page 341, may conveniently be used in place of Poggen-
dorft's method.
134. Calibrating a (ralvanometer by Employing
Known Resistances and a Cell of Constant E. M. F.
— We have seen, in § 26, page 58, that a galvano-
meter can be calibrated by direct comparison with a
tangent galvanometer ; also in § 30, page 64, that when
the controlling force is that produced by a uniform
magnetic field, and when also the galvanometer can be
easily turned backwards and forwards round its centre,
the employment of the sine principle enables us to cali-
brate it without the use of any other galvanometer. We
have also seen, in § 96, page 164, that when we have no
other galvanometer at hand that has been already cali-
brated, and when the galvanometer cannot be moved
without interfering with its adjustment, which is generally
the case when we are employing a galvanometer with fibre
suspension and levelling screws, we may calibrate the gal-
vanometer by employing known resistances, when a con-
stant P. D. is maintained at the terminals of the circuit.
The same thing may be done without having a con-
stant P. D. between the terminals (Fig. 61, § 96, page
165), if we have a coll of constant E. M. F. of E volts
instead. Let h ohms be the resistance of the cell, then, if
c?i°, c?2°, c?3°, &c., be the deflections on the galvanometer,
when 7*1, 7*2, r^,, &c., ohms are the resistances respectively
in R, we know that the currents producing these deflec-
tioMis are respectively
E E E .
-, &c., amperes,
b -\- g ■\- r^ h -\-g -^-r^ b + g -\- r^
Chap, v.]
ARRANGEMENTS OF CELLS.
239
so that an absolute calibration curve can be drawn for
this galvanometer.
If the E. M. F. of the cell is not known in volts, but
if we are sure that it is constant, we can draw the rela-
tive calibration curve, although not the absolute one.
In order to see quickly the kind of law connecting
deflection and current for any particular galvanometer,
it is convenient in making this experiment to select
values of R, such that b -\- g + r^ equals ^ {h -\- g -\- r^),
(b + g -\- r.^) equals i (b -h g + fi), &c., since in that
case the second current is double the first, the third
thrice the first, &c. Of course r^ should be chosen so
that the deflection corresponding with this resistance is
a conveniently small one, for example, about 10° in an
ordinary galvanometer having a scale reading up to 90°
135. Arrangements of Cells. — A battery may be
formed of galvanic cells, or elements, as they are some-
mm^M
Fig. 89.
fig. 90.
Fig. 91.
times called, in a variety of ways. All the cells may
be "in series," as in Fig. 89, or they may be joined up
all "in parallel," as in Fig. 90, or '^partly hi series
and partly in parallel," as in Fig. 91. These three
arrangements are symbolically shown in A, b, c (Fig. 92),
where the long thin lines stand for the plates in the
240 PRACTICAL ELECTRICITY. [Chap. V
battery from which the positive electricity flows ; or,
with the definition of direction of current we have
already adopted, the current flows in the circuit out-
side the battery from the plate represented by the long
thin line to that represented by the short thick line,
while in the battery itself the current flows from the
short thick line to the long thin one.
For example, in the DanielVs cell, which consists,
as previously described in § 119, page 210, of a plate of
copper in a solution of copper sulphate, separated by a
Fig. 92.
porous diaphragm of imglazed earthenware from a
plate of zinc in a solution of zinc sulphate, the long
thin line represents the copper plate, and the short thick
one the zinc plate ; the wavy line in each case stands
for the copper wires attached to the copper and zinc
plates respectively. In the Grove's cell, consisting, as
we have seen in § 124, page 218, of a platinum plate
in strong nitric acid, separated by a porous cell from
a plate of zinc in dilute sulphuric acid, the long thin
line represents the platinum plate, and the short thick
line the zinc plate. In a Bunsen^s cell, which, as ex-
plained in § 125, page 219, differs only from a Grove's in
that the platinum plate is replaced by a carbon one, the
long thin line stands for the eurbon plate.
When all the cells are in series, the total current
produced by the battery passes through each cell; there-
Chap, v.] E. M. P. AND RESISTANCE OF BATTERIES. 241
fore it follows, from what has preceded (§ 115, page 203),
that the E. M. F. of the battery is equal to the sum of the
E. M. Es. of each of the cells. If, on the other hand, the
cells are joined up all in parallel, the current divides itself
between the cells ; and if the cells are all made with the
same materials, but not necessarily of the same size nor of
the same internal resistance, the total chemical action, and
therefore the total amount of fuel burnt per second, is
exactly the same as if the entire current went through
one of the cells. Hence the E. M. F. of the battery is
simply that of any one of the component cells. The
resistance, however, of the battery will be less than
that of one cell, as the road for the current through the
battery is made wider by putting cells in parallel ; and
if the cells have each the same resistance of h ohms, and
if there be p of them in parallel, the resistance of the
battery is — ohms. If the cells be partly in series and
partly in parallel, we must combine the last two sets of
conclusions, so that if the E. M. F. of each cell be e volts,
and if there be s cells in series, and p in parallel, the
total E. M. F. of the battery E, and the total resistance
B, will be given by
E = s e volts,
B = — ohms:
p
so that if A be the current in amperes which the battery
sends through an external resistance r,
A se
P
In order to experimentally test the accuracy of these
results, a number of cells, freshly put together, and having
their corresponding plates of the same size^ the plates in
the different cells at the same distance apart, and the
amount of liquid in each cell the same, should be joined
Q
242 PRACTICAL ELECTRICITY. |Chap V.
up in a variety of ways, and tlie resistances of the com-
binations measured, as well as the E. M. Fs. of the bat-
teries compared with the E. M. F. of a single cell, selected
at random from the battery, by one or other of the methods
of testing previously given. The cells should be of such
a type that the E. M. F. of each cell is a constant, a con-
dition very satisfactorily fulfilled with DanielFs cells^ and
to avoid the cell used as the standard having a higher or a
lower E. M. F. than the average E. M. F. of the cells
employed, different cells may be selected from the com-
bina,tion as the standard cell in the different experi-
ments.
Example 58. — To find the current that twelve
DanielFs cells, each having a resistance of 0*6 ohm and
an E. M. F. of 1"1 volt, can send through an external
resistance of 5 ohms if the cells be formed four in series
and three parallel :
A = -iA±L
3
Answer. — 0*76 ampere.
Example 59. — How many such Daniell's cells must be
used in series to send a current of 1 ampere through an
external resistance of 8 ohms, if one line of cells in series
only be employed %
Let X be the required number of cells, then
_ ^ X 1-1
~ 8 + « X 0-6'
.-. aj=16.
Example 60. — If in the last question the cuirent be
2 amperes instead of 1, then how many cells will be
required ?
a3 X 1-1
2 = -— ,
8 + aj X 0-6
,\x= -160.
Chap, v.] EXAMPLES. 243
Therefore no number of such cells put in one line in
series could send this current. In fact, if one cell be
short-circuited with a piece of thick wire, the current it
will send will be ——, or 1-83 amperes, and this is the
maximum current one, or any number of cells, arranged
simply in series, can send. For if there be n of them
arranged in series, and the whole be short-circuited, the
current will be -— or 1-83 amperes, or, simply, the
current sent by one cell when short-circuited. Hence, if
there be any external resistance, the current sent by one
row of these cells in series, no matter how many there
may be in the row, will be less than 1 -83 amperes.
Example 61. — Forty exactly similar cells, each having
dn internal resistance of f ohm, when joined in series send
a current of 0*5 amperes through an incandescent lamp
of 80 ohms' resistance : how many cells in series would
be required to produce the same current through each of
two such lamps arranged in parallel ?
Let e be the E. M. F. of one cell in volts, then
40 X e _
80 + 40 X 0-75 ~ *'
.-. e= 1-375 volts;
therefore J if x be the required number of cells,
X X 1-375
80
— + XX 0-75
2
1.
since the resistance of the two lamps in parallel will be
80
— - ohms, and they will require together 1 ampere,
.-. a; =64.
136. Arrangement of a Given Number of Cells to
produce the Maximum Current through a given Ex-
244 PRACTICAL ELECTRICITY. [Chap. V
ternal Resistance. — If N be the total number of cells
employed in a battery, p being arranged in parallel, and
s in series,
and the formulae on page 241 may be written
r + —
If, therefore, we desire to ascertain what arrangement of
a definite number of cells, each having a fixed E. M. F. of
e volts, and internal resistance 6 ohms, will give the
greatest current through a fixed external resistance of r
ohms, we must ascertain what value of s will make the
last expression a maximum. But to do this by trial by
calculating the value of A corresponding with each of
a very large number of values of s would be extremely
laborious, and a far better plan for those who are not
acquainted with the difierential calculus is as follows : —
Give numerical values to e, r, and — , let them for example
be 2, 3, and 4, then the expression becomes
28 .
3 + 4s2'
next draw a curve having the values of s for the abscissae,
and the corresponding value of the expression for the
ordinates, and ascertain, from the shape of the curve, for
what value of s the expression has its maximum value,
then that value of s is the value required. In selecting
values for s, a certain amount of practice is, of course,
necessary, in order to select the best values, but one may
be guided by remembering that if on taking two or three
values of s we obtain practically the same value for the
expression for A, it can be no use taking intermediate
values of s.
The curve obtained for A has the general shape shown
Chap, v.] MAXIMUM CURRENT, FIXED EXTL. RESISTANCE. 245
in Fig. 93, the values of A being calculated on the sup-
position that e, r, and — , have the values 2, 3, and 4 re-
iS
Fig. 93.
spectively, and we find that the value of s that makes A
a maximum is about 0'85, and this is the value of s
which makes ^25
246 PRACTICAL ELECTRICITY. [Chap. V.
or, in other words, the proper arrangement of a given
number of cells to send the maximum current through
a given external resistance is that which makes the re-
sistance of the battery equal to the external resistance.
The curve falls more slowly for values of s greater
than that which makes A a maximum than for values less
than this, and this tells us that the current will be not
so much lessened by making s too large as it will be by
making it too small ; hence if the number of cells and the
resistance of each are such that it is impossible to arrange
the battery so that its internal resistance is equal to
the fixed external resistance, it is better, when the ex-
ternal resistance is midway between the resistances the
battery has when arranged in these two ways, to select the
arrangement that puts rather too many cells in series
than the one that puts rather too many in parallel. For
example, suppose we have twelve cells, each having a re-
sistance of 3 ohms, and we desire to arrange them so
that they send a maximum current through an external
resistance of 3i ohms, if we arrange them three in series
and four in parallel, the resistance of the battery will be
3x3 „,■
— - — or 2± ohms,
4
on the other hand, if we put them four in series and
three in parallel, the resistance will be
— - — or 4 ohms ;
o
and the given external resistance of 3| ohms is exactly
half-way between 2J and 4. Let us consider the cur-
rents produced by these two arrangements of the cells.
With the first,
if e be the E. M. F. of each cell in volt?. With the second
arrangement,
Chap. V.J EXAMPLES. 247
A = J^~^ amperes.
24 32
The first reduces to — e and the second to — e ampere,
8
and of these the second is the greater by e of an
ampere.
Example 62. — What is the least number of Grove's
cells, each having an E. M. F. of 1 '8 volts, and an inter-
nal resistance of 0*09 ohm, that must be arranged in
series to send half an ampere through a 50 volt incan-
descent lamp 1
This question may be solved in two ways — we may
either first find the resistance of the lamp and then the
number of such Grove's cells that it is necessary to put
in series to send half an ampere through this external
resistance — or we may consider what is the P. D. at the
terminals of such a Grove's cell, when hali an ampere is
passing through, and hence deduce how many such cells
must be put in series so that when half an ampere is
passing through them, the P. D. at the terminals of the
battery is 50 volts.
50
1. The resistance of the lamp = — ohms,
= 100 ohms,
, • . if n be the required number of cells,
1 ^ nx 1-8
2 ~ w X 0-09 + 100'
.'. n =28-5.
Hence, 28 cells would produce rather too small a current,
and 29 rather too much. We should have, therefore, to
choose between using 28 cells and having the lamp not
quite bright enough, or using 29 cells and having it a
248 PRACTICAL ELECTRICITY. [Chap. V.
little too bright, or using 29 cells and interposing a
small resistance by means of a piece of wire or in any
other convenient way.
2. If n be the number of cells in series, then from
§ 116, page 206, the P. D. maintained at the terminals
of the battery equals
w X l•8-lr^ X 0-09.
And this is to equal 50.
Hence,
71 X 1-8-1 w X 0-09 = 50,
which is the same equation as was used before, and there-
fore must lead to the same value of n.
Example 63. — If 29 cells were used in series in the
last question, what must be the value of the added re-
sistance, so that the current through the lamp may be
exactly half an ampere ?
Let X be the required resistance in ohms, then
1__ 29 X 1-8^
2 "" 29 X 0-09 + 100 -h X
.', X = 0-895 ohm.
Example 64. — If four incandescent lamps, each re-
quii'ing half an ampere, and 50 volts P. D. maintained
at the terminals, are to be fed with Grove's cells, each
having an E. M. F. of 1 -8 volts, and an internal resist-
ance of 0-1 ohms, what arrangement of cells and of
lamps will require the least number of cells to be used 1
First, let the four lamps be put in series, and let al]
the cells, n in number, be in series, then the P. D. at the
terminals of the battery must be 4x50, and
w X 1-8 - iw X 0-1 = 4 X 50,
.'. w= 114-3.
Next, let all the lamps be put in parallel, and all the
Chap. V.J EXAMPLES. 249
cells in series, then the total current required will be
4 X i or 2 amperes, therefore
n X l-8-2n x 0-1 = 50,
.-. n= 31-2;
hence, 32 cells, with a small resistance interposed, would
give the required current, and this arrangement of all
the lamps in parallel would only require about one-
quarter of the number of cells necessary if all the lamps
were in series.
Various other cases might be tried ; for example,
the lamps two in series, and two in parallel, or the cells
two in parallel and half in series; but it would be found
that all the cells, in series, and all the lamps in parallel,
is the best arrangement.
Example 65. — If 40 such lamps as are referred to in
the last few questions instead of 4 had to be fed with
Grove's cells, what would be the best arrangement of the
cells and of the lamps 1
First, let us try all the lamps in parallel, and all the
cells in series, which arrangement we found was the best
in the previous case, then, as the total current required
will be 40 X J or 20 amperes, and the P. D. at the ter-
minals of the battery 50 volts,
w X 1-8 - 20n X 0-1 = 50,
or n = — 250,
a negative answer. This means that no number, no matter
how great, of such Grove's cells, if the cells were arranged
in series, could feed 20 such lamps if arranged in parallel ;
and the reason of this is clear, because, if one Grove's
cell were simply short-circuited, the current that it would
produce would be
— or 18 amperes,
hence, no number of such Grove's cells arranged in series
can produce more than 18 amperes, even if short-oir-
250 PRACTICAL ELECTRICITY. [Chap. V.
cuited, and hence they can only produce less than 18
amperes if there be any external resistance, whereas we
want them to produce 20 amperes.
Secondly, let us try half the lamps in parallel and two
in series. In that case the total current must be 10
amperes, and the P. D. 100 volts.
Hence we have
n X l•8-10 9^ X 0-1 = 100,
or n = 125.
We may now try all the lamps in parallel and half
the cells in series, and two in parallel. Let n be the
number in series, that is, half the total number, then
n X 1-8-20 "L^L^ = 50,
2
. • . n = 62-5.
Consequently the total number of cells required is 125.
Hence, whether we put the 40 lamps two in series and
20 in parallel, and use all the cells in series, or put half
the cells in series and two in parallel, and use all the
lamps in parallel, exactly the same number, 125, of cells
is required.
There is one other arrangement that might be tried,
viz., all the lamps and all the cells in series, but from
what we saw in the first part of example No. 64, we may
anticipate that this will be a very bad arrangement.
With this arrangement the current required will be half
an ampere, the P. D. 40 x 50 volts,
. •. nx 1-8-1 n X 0-1 = 2,000,
or n = 1,142-9.
Hence 1,1 43 cells would be required with this arrangement.
Example 66. — How many Daniell's cells, each having
an E. M. F. of 1-1 volts, and an internal resistance of
0-8 ohms, would be required to feed two Edison incan-
descent lamps, each requiring 0-75 of an ampere, and 110
volts at its terminals 'i
Chap, v.] EXAMPLES. 251
One such Daniell's cell, short-circuited, would produce
— or 1-375 amperes,
0-8
hence, if we put the lamps in series, one row of Daniell's
cells in series will produce sufficient current. If, how-
ever, we put the two lamps in parallel, then, since the
total current must be 1*5 amperes, we must have two
rows of cells.
First, let the lamps and cells be in series, then
n X M-0-75W X 0-8 = 220,
or 71 = 440.
Second, let the cells be half in series and two in
parallel, and let n be the number in series, the lamps
being still in series, then
ny. 1-1-0-75^ M =,220,
2
or w = 275.
Hence, the total number of cells necessary will be 550,
or this arrangement is worse than the preceding.
Third, let the cells be half in series and two in
parallel, but let the lamps be also in parallel, then
V, 1 1 1 Fi w X 0-8 TT^
n X ri — 1-5 = 110,
2
or n = 220.
Hence, the total number of cells required is 440, or the
same as in the first case.
Fourth, let the cells be three in parallel and n in
series, and let the two lamps be still in parallel, then
n X 1 -1 — 1-5 r= 110,
3
.'. n= 157-1,
and the total number of cells required would be 472.
252 PRACTICAL ELECTRICITY ) [Chap. V.
Therefore, arrangements Nos. 1 and 3 require the
least number of cells, but with any arrangement the
number of Daniell's cells required is very large in con-
sequence of the high resistance of the cells, and of the fact
that the greater part of the energy is expended in send-
ing the current through the cells themselves.
Example 67. — How many lamps in parallel, each re-
quiring 80 volts, and 0*6 of an ampere, can be fed with
42 accumulators in series, each having 1*95 volts E.M.F.
on discharging, and 0'005 ohms' internal resistance I
Let I be the number of lamps, then, since the total
current will be I x 0'6, we have
42' X 1-95- Z X 0-6 x 42 x 0-005 = 80.
Answer. — 15.
Example 68. — If the number of accumulators in the
last question be increased by one, by how many may the
number of lamps be increased %
Answer. — The number of lamps may now be 29*8,
that is, may be 30 all a trifle too dull, or 29 a trifle too
bright, unless a small resistance be introduced. The ad-
dition, therefore, of one accumulator practically doubles
the number of lamps that can be fed by them.
Example 69. — If there be 44 accumulators in series,
and if 46 lamps be fed by them, each lamp requiring, as
before, 80 volts at its terminals, and 0'6 of an ampere
passing through it when properly glowing, how much
per cent, will the current passing through the lamps be
too great or too small 1
80
The resistance of each lamp is — or 133-3 ohms, hence
133'3
the resistance of all the lamps will be or 2-899
46
ohms, consequently the current passing through them
will be
Chap, v.] VARIATION IN TOTAL CURRENT BY SHUNTING. 253
4ixl-95
44 X 0-005 + 2-89J
or 27-51
amperes,
The current that ought to pass through the lamps
is 46 X 0-6, or 27-6 amperes. Hence the current is
about 0*3 per cent, too small.
137. Variation produced in the Total Current by
Shunting a Portion of the Circuit. — We can now cal-
culate the entire effect produced on the current passing
through a galvanometer of resistance g, by shunting the
galvanometer with a shunt of resistance s. Let E be
the E. M. F. in volts, and b the resistance in ohms, of a
battery, r the resistance in ohms of the rest of the cir-
cuit, excluding the galvanometer, and g the resistance of
the galvanometer ; then, before shunting, the current G^,
in amperes, that passes through the galvanometer, is
simply the whole current A^, that passes through the bat-
tery, and this equals
E
, amperes.
After shunting, the current A^, now flowing through the
battery, becomes ^
amperes,
b + r +
s + 9
and the fraction of this passes through the galva-
s + g
nometer ; therefore, if Gg be the current now "passing
through the galvanometer.
G, =
E
s-hg
gE
' {8+g)(b + r) ^8g
254 PRACTICAL ELECTRICITY. [Chap. V.
If b -\- r be very large compared with g^ then,
approximately,
G,
=
s
8+9
E
6 + r'
and Ag
=
E
6 + /
also A,
=
E
b + r'
.-. G,
=
s
A„
that is to say, the current passing through the battery
and through r is practically unchanged by shunting the
galvanometer, and, therefore, after the galvanometer has
been shunted, it is not merely the fraction of Ag,
s + g
but of A^, that passes through the galvanometer.
s -\- g
On the other hand, if 6 + ^ be small compared with
gy then, approximately,
89
= ^
E
and Gj = Ai = — ,
9
. • . Gg = Gi approximately.
Hence, as long as is large compared with & + r,
that is, as long as the shunted galvanometer is the major
part of the whole resistance in the circuit, shunting the
galvanometer produces no diminution in the current
flowing through it. And it is not until the resistance
Chap. V.l RXAMPLES. 255
of the shunted galvanometer is reduced to a value com-
parable with 6 + r, that the galvanometer deflection is
seriously diminished.
Example 70. — If the resistance of a galvanometer be
1,000 ohms, what must be the resistance of a shunt to
diminish the current passing through the galvanometer
to one-half, first, when the resistance of the rest of the
circuit is 100,000 ohms; secondly, when it is only 100
ohms?
In the first case we have
sE 1 E
(s + g){h -\-r)-^sg 2 h + r ^- g
or substituting
1 1
= - X
{s + 1,000) X 100,000 -h « X 1,000 2 101,000*
. •. s = 990-1 ohmsj
that is, 8 is only a little less than 1,000 ohms, which
is the resistance of the galvanometer.
In the second case
(«+ 1,000) X 100 + s X .1,000 2 1,100*
. •. s = 90*9 ohms,
or not as much as one-tenth of the galvanometer re-
sistance.
Example 71. — What must be the resistance of a
galvanometer relatively to that of the rest of the circuit,
so that shunting the galvanometer with a quarter of its
own resistance may halve the current passing through it 1
From what has preceded, we have
s 1 1
(8 + g){h^r) + sg 2 6 + r -f /
256 PRACTICAL ELECTRICITY. [Chap, V
and since s = -f- »
4
i ..ix—l
+ 9)(b + r) +f
l4.o\U^A , El 2 b^r+g
. • . g = 3 (b +r).
Example 72. — In example No. 38, given on page
180, what resistance must be added to the main circuit,
so that the insertion of the shunt shall not alter the total
current 1
To solve this question we must consider by how much
the resistance of the circuit has been diminished by the
insertion of the shunt, this diminution being, of course,
equal to the difference between the resistances of the
galvanometer shunted and unshunted.
The shunted galvanometer has a resistance of
1,808 X 452
1,808 + 452 *
or 361 "6 ohms,
therefore the resistance of .the circuit has been diminished
by 452 — 361-6, or 90*4 ohms, and this resistance must be
added if we wish that the total current shall be kept
constant.
Example 73. — What resistances must be added to the
main circuit to keep the total current constant when a
galvanometer, having 1,000 ohms' resistance, is shunted
with the three shunts which respectively allow Toth,
i^th, and Toootli of the current to flow through the
galvanometer 1
If s be the resistance of the shunt, and g the resist-
ance of the galvanometer, the diminution of the resistance
produced by shunting the galvanometer is
Chap. V.J CONSTANT TOTAL CURRENT SHUNTS. 257
g- 1^., OV^L.
s-\- 9 s -\- g
From what has been given in § 104, page 178, the lesist-
, 1000 1000
ances of the three shunts must be ~^' ~^~» ^^^
ohms respectively. Therefore, the resistances that
y yy
must be added are
10002
]^ + 1000
9
or 900 ohms.
1^^0^_ or 990
l^ + 1000
99
10002_ ^^ 9,9
1^^^ + 1000
999
138. Constant Total Current Shunts.— There are two
ways, differing somewhat from one another, by means of which a
box of shunts can be so arranged that the insertion of the shunt
coil, parallel to the galvanometer, also introduces a compensating
resistance in the main circuit, and so keeps the main current un-
altered in strength. The first of these is due to Mr. Kempe, and.
the second to Mr. Rymer Jones.
Fig. 94 shows symbolically Mr. Kempe's arrangement, and it
will be seen that the insertion of a plug into one of the holes
A, B, C, for the purpose of introducing a shunt parallel to the
galvanometer G, also adds one or more of the resistances i\, rg, r^,
to the main circuit, whereas, if the plug be inserted in the hole
which is not lettered, the galvanometer is unshunted, and all the
three coils ri, r^, r^, are cut out of the circuit. A plan of the
actual shunt box is seen in Fig. 95.
To determine what should be the values of these resistances,
we have to remember that, if Wj, «j, Wg be the three multiplying
B
258
PRACTICAL ELECTRICITY.
LChap. V.
powers of the shunts, so that the three currents d, Gg, G-g, passing
c c c
through the galvanometer are respectively equal to — , — , — ,
Wi
■where C is the total current in each case, the resistances of the
Fig. 94.
^ real size
Fig. 95.
shunted galvanometer are in the three cases i^ , ^ , -^ if c
% ^1-2 %
be the resistance of the galvanometer itself. In order, therefore,
that the total resistance in the circuit may be constant, we must
have
^ + ^1
^2 -Vr-i — g
and r,=g - 9 + r^-¥\
From which it may be shown that
^3
n —
■»,{n.,-\)
%(%-!)
X <?,
9-Vi,
Chap. V.J CONSTANT TOTAL CURRENT SHUNTS.
269
n =
xa-r^-rs.
Also that s, = — ^,
«i — 1
tii(n2-l)
Example 74. — If the galvanometer have a resistance of 5,000
ohms, and if we wish either the ^^jth, or the y^^th, or the toVo^^
Fig. 96.
of the total current to pass through the galvanometer, what must
he the resistances of s,, S2> *3? ^i) **2> and 73 ?
^l» "a> "3?
Answer.— Sj^ = 5-006, s^ = 50-964, i
- 504 -545, and r-i = 4,445*000 ohms.
616-667, ri = 45-455,
Fig. 96 shows, symholically, Mr. Rymer Jones's arrangement.
To use it two plugs have always to he inserted in the holes marked
with the corresponding figures. If the plugs he inserted in the
two holes marked 1, we have a shunt equal to a and a resistance
added to the main circuit equal io b -\- c -\- d. If the plugs he in-
serted in the two holes marked 2, then we have a shunt equal to
a-\- b and a resistance c -\- d added to the main circuit, &c. Hence,
it follows that
260 PRACTICAL ELECTRICITY. [Chap. V.
a =
Wo-1
a-\-b-\-c =
— 3
d-\-e = !!3i:I xg,
from which, a, b, c, d, e can he easily calculated for any particular
values of g, «,, «2j and %.
If one of the plugs he inserted in the hole marked 4, the cir-
cuit will he completed through the galvanometer unshunted.
Example 75. — If the galvanometer have a resistance of 5,000
ohms, and we wish either the -j^th, or the y^th, or the ip^^th
of the total current to pass through the galvanometer, what must
he the resistances of a, b, c, dy and e ?
Answer.— a = 5006, b = 45-500, c = 505-060, d = 4,444-94,
and e = 55-06 ohms.
Fewer coils are, therefore, required with this second arrange-
ment, hut it has the slight disadvantage that it requires two plugs
to he inserted instead of only one as with Mr. Kempe's arrange-
ment.
139. Independence of the Currents in Various Cir-
cuits in Parallel. — From what has preceded it follows
that if a, c, d, &c. (Fig. 97) be circuits in parallel
with the battery 6, the currents A, C, D, &c., passing
through the circuits respectively, will be each indepen-
dent of the stoppage, or variation, of any, or of all,
of the other currents, as long as the combined resistance
of the circuits, that is,
1
- + - + - 4 &c..
a c a
Chap, v.] INDEPENDENCE OF CURRENTS IN PARALLEL. 261
is large compared with the resistance of the battery, h.
Because the current through any one of the circuits
simply depends on the potential difference at the terminals
of the battery, and on the resistance of the particular
circuit. The latter is, of course, not altered by altering
the resistance of any or of all the other circuits, and the
potential difference at the terminals of the battery re-
mains constant when the above relationship of resistance
is fulfilled.
Practically, therefore, in all cases where a generator
of very small internal resistance is employed, the currents
in various parallel circuits fed
by it are all independent of one
another. And this is one of the
great advantages of the very
small resistance of " accumiv-
lators^^ or ^^ secondary batteries"
or ^^ storage cells" as they are
differently called, for electric
lighting, in that any one of a
number of lights fed in parallel ji^g 97^
by these cells can be turned on
or off without materially altering the intensity of the
light given off by any one of the remainder.
It also explains why Grove's cells, which, as stated in
§ 124, page 219, have a small resistance compared with
Daniell's, Minotto's, and other well-known cells, were
used in the early days in telegraph ofiices, when the
different messages used to be sent along several tele-
graph wires with one battery. The trouble and expense,
however, involved in keeping the Grove's cells in order
caused the plan of working several telegraph wires with
one battery to be abandoned in favour of having a sepa-
rate battery of much higher resistance to work each line
independently. But the invention of accumulators by
Plante, and the improvements that have been effected in
them by Faure, Swan, Sellon, Volckmar, and others,
during the last few years, are leading to a return to the
262 PRACTICAL ELECTRICITY.* [Chap. V
old plan of several telegraph wires being worked with
one current generator.
Example 76. — If three telegraph wires, having re-
sistances of 200, 250, and 300 ohms respectively, in-
cluding in each case the resistance of the "receiving
instrument" or the instrument by means of which the
messages are received, be worked by one battery having
a resistance of 20 ohms, by how much per cent, will the
current passing along the first line, when no current is
passing along either the second or the third lines, be
altered : 1st, by a current being sent along the second
also ; 2nd, by a current being sent along both the second
and the third lines, in addition to the one sent along
the first?
If E be the E. M. F. of the battery in volts, then the
current Cj, flowing along the first line when no current is
flowing along either the second or the third, is
If a current is also being sent along the second wire,
the total current flowing through the battery is
E
amperes,
2Q 200 X 250
200 -f 250
and of this the current Cg, flowing along the first line> is
250 ^ E
200 -f- 250 20 + 200 x 250 '
200 + 250
250E
20(200 + 250) + 200 x 250 ^"^P®^®^*
Similarly, if a current is also being sent along the third
^ line, the current 0^, flowing along the first line, is
Chap, v.] EXAMPLES. 263
1
200
E
200 250 300
amperes.
30 +
200 250 300
Therefore,
^' ^ 220 ^""P^"^*^
^' = 236 "
and
^' - 249-4 "
Hence, C^ is diminished by about 6 -8 per cent, by allow-
ing a current to flow along the second line, and by about
11*7 per cent, by allowing a current to flow along both
the second and the third lines.
Example 77. — If two telegraph lines each have a
resistance of 500 ohms, including the resistances of the
receiving instruments, what may be the greatest resist-
ance of the battery employed to send the current along
both, so that the current flowing along either shall not
be diminished by more than 1 per cent, by sending a
current also along the other 1
Let E be the E. M. F. in volts, and b the resistance
of the battery in ohms, then the current flowing along
either line, when no current is being sent along the
other, is
E
; — — amperes:
6 -f 500 ^
and the current flowing along either line, when a cur-
rent is also being sent along the other^ is
2 bT^Eb *'"P^''^'
264 PRACTICAL ELECTRICITY. [Chap. V
Now we want h to be of such a value that
E IE is not greater 1
. E
6 + 500 2^h^- 250 than IQO
6 + 500
Consequently, the largest permissible value
found by making
of 6 will be
E 1 E 1
X — X
E
6 + 500 2 6 + 250 100
6 + 500 '
or ^^ - 1 - 1 -
1 .
100 6+500 2
6 + 250
Answer.—
-5*1 ohms.
Example 78. — There are two telegraph lines, one
having a resistance of 400 ohms, and .the other of 500
ohms, including the resistance of the receiving instru-
ments. The receiving instrument on the first line is so
arranged that it will work without adjustment, with cur-
rents varying between 5 and 5*2 thousandths of an am-
pere. What must be the E. M. F. of, and resistance of,
the common battery, for the two lines, so that the cur-
rent flowing along the first line may be always between
these limits, whether or not a current is being sent along
the second line 1
If E be the E. M. F. in volts, and 6 the resistance in
ohms of the battery, the maximum current flowing along
the first line will be
E
amperes,
6 + 400 ^^^^^^^^^'
and the minimum
current
500
X
6 +
E
an
400 + 500
400 X 500
400 + 500
or
500 E
900 6 + 200,000
Chap, v.] EXAMPLES. 265
The first current must not exceed 6'ti thousandths of
an ampere, and the second must not be less than 5
thousandths of an ampere. Taking, therefore, the limit-
ing values, we may say that
E 52
and
b + 400 10,000
5E 5
9b + 2,000 1,000
Solving these two equations for E and b, we find
that
E = 2-19 volts about,
and b = 21 ohms „
In practice, larger E. M. Fs. than this must be used
to allow for leakage along the line_, in consequence of
which only a portion of the current that leaves the send-
ing or signalling end arrives at the receiving end.
Example 79. — If 10 of the 30 lamps in example 68,
page 252, be turned out, what will be the P. D. at the
terminals of the remaining 20 ?
Answer. — 81-27 volts.
Example 80. — If 50 or more incandescent lamps in
parallel, each requiring 0-8 amperes and 100 volts to
glow properly, be fed with 55 accumulators in series,
each having an E. M. F. of 1*98 volts when discharging,
what must be the resistance of each accumulator, and
what is the maximum number of lamps that can be
lighted, so that the P. D. at their terminals never ex-
ceeds 101, and is never less than 99 volts?
The resistance of each lamp may be taken as
or 125 ohms. Hence, considering the case of the least
number of lamps, ' 50, which will correspond with the
highest number of volts, 101, we have, if b be the resist-
ance of one accumulator.
266 PRACTICAL ELECTRICITY. [Chap. VI.
55 X 1-98 _ 101
555+11^" 11^'
50 50
from which it follows that h = 0*003555 ohms.
Next, considering the case of the largest number of
lamps n, which will correspond with the lowest number
of volts allowed, viz. 99, we have
55 X 1-9 99
R., , 125 125
55 6 +
n n
Substituting in this the value previously found for 6,
and solving for n, we find that
n = 63-92.
Hence, 64 lights would be practically the largest
number.
CHAPTER VI.
INSULATION.
140. Surface Leakage, and Leakage through the Mass— 141. Coating
Insulating Stems with ParafiBn Wax, or Shell-lac Varnish —142.
Sealing up One End of a Cahle when under Test — 143. Construc-
tion of an Insulating Stand — 144. Laws of Surface Leakage, and
of Leakage through the Mass — 145. Corrugating the Sides of
Ebonite Pillars — 146. Common Fault made in Constructing
Ebonite Pillars — 147. Telegraph Insulators — 148. Testing Insu-
lators during Manufacture — 149. Measuring High Resistances —
150. Subdividing a P.D. into Known Fractions — 151. Constant
of a Galvanometer — 152. Very Delicate Galvanometers— 153.
Thomson's Astatic Galvanometers — 154. Importance of the Gal-
vanometer being Well Insulated.
140. Surface Leakage, and Leakage through the
Mass. — There are two ways in which electricity may
pass from one body to another ; it may either creep along
Chap. VI.] LEAKAGE. 267
a layer of dirt and moisture on the surface of an
insulating rod, or it may pass through the mass of the
insulating material. The former may be called " surface
leakage ^\- and the latter, '-Heakage through the mass."
In the case of a charged body supported on a rod of glass
or ebonite, surface leakage is the main thing to guard
against ; whereas, with a long submarine cable, consisting
of a copper conductor surrounded with guttapercha or
with indiarubber, and immersed in the sea, the main loss
of electricity is through the guttapercha or indiarubber.
If, however^ the piece of insulated cable be very short,
then the surface leakage at the ends, arising from the
electricity creeping
from the ends of the
copper conductor
over the ends of the
guttapercha covering Pig. 98.
to the water or the
iron sheathing which is outside the guttapercha, may
be the cause of the most important part of the loss.
Hence, when it is desired to test the actual passage
of the electricity from the conductor through the in-
sulating material, it is usual, in order to diminish the
surface leakage to a minimum, to cut the end of the
core like a pencil, as shown in Fig. 98, so as to expose
a long freshly bared, clean, dry surface of guttapercha
or indiarubber. The insulation of the end can be still
further improved by coating the surface with a thin
layer of clean paraffin wax, which has been first melted
by heating, to a temperature not however much above
that of boiling water, otherwise the wax would be par-
tially decomposed, and its resistance diminished,*
141. Coating Insulating Stems with Paraffin Wax
or Shell-lac Varnish. — Coating the surface of any insu-
lating stem which is exposed to the air with paraffin wax
* To avoid the paraflSn wax being overheated, it is well to warm
the vessel containing it by means of a water hath in the same way that
glue is usually heated in an ordinary glue-pot.
268 PRACTICAL ELECTRICITY. (Chap. VI
has not only the advantage that it renders the surface
much less '■^ hygroscopic^^ or attractive of moisture, but
it enables the wax to be easily partially scraped off at any
time, and a new clean dry surface exposed. Shell-lac
varnish, made by dissolving shell-lac in alcohol, may be
employed in the place of paraffin wax, but, in many
cases, it is not as good, partly because shell-lac, being
hard and brittle, cannot be easily scraped so as to expose
a new clean surface, and partly because, at the present
day, it is very difficult to buy really good shell-lac_, the
material of commerce being much adulterated.* If,
however, a glass rod can he kept free from dust, and
artificially dried, then it is better to put neither paraffin
wax nor any kind of varnish on it.
142. Sealing up One End of a Cable when under
Test. — The insulation of a cable may be tested by
measuring with a very delicate galvanometer the
current that a battery of high E. M. F. can send
through the indiarubber, guttapercha, or other insu-
lating material used in its construction. To do this
it is only necessary to have one end of the copper
conductor bare, hence it is desirable after pointing the
guttapercha at the other end, as shown in the last figure,
to seal it up altogether by dipping it into paraffin wax
two or three times, so as to cause a lump of paraffin wax
to adhere to it, which can be best done when the paraffin
wax has cooled until it is approaching the temperature
of solidification.
143. Construction of an Insulating Stand. — In
Fig. 29 the plate a, and in Fig. 40 the pot p, are
supported on a special form of insulating stand, in which
* Dr. A. Muirhead, who has had great experience in the use of
8hell-lac in the construction of condensers, recommends the following
process for obtaining good insulating varnish. Obtain " button " lac,
pick out the cleanest lumps, and dissolve them in absolute alcohol.
Allow the solution to stand for some time, and use only the w/)per part
of the solution. When the highest insulation is required, first dissolve
the button lac in ordinary alcohol, and precipitate it by allowing the
solution to trickle into distilled water, then dissolve the precipitate
in absolute alcohol.
Chap. VI.J INSaLATING STAND. 269
the glass rod is kept /reeyrom dtist and artificially dried.
This device for obtaining high insulation is far superior to
the old-fashioned plan of using a simple rod of glass or
ebonite, since such a rod, whether it was coated with
varnish or not, required perpetual cleaning and drying to
prevent the electricity leaking down its surface. The
special arrangement shown in these figures, and which
has been designed by the author for experiments on
statical electricity, consists of a glass vessel made of any
convenient kind of glass, and having at its bottom a
tubulure of glass attached vertically at the centre. This
tubulure, or collar, of glass is ground inside like the
inside of the neck of a glass-stoppered bottle, and into this
tubulure the ground end of a rod of highly insulating
glass fits, much in the same way as a glass stopper does
into a bottle. On to the top of this glass rod anything can
be fixed ; for example, the plate A (Fig. 29), and the
pot p (Fig. 40), are supported in position by a little
collar of metal, which is soldered to the bottom of A and
of P, and which slips fairly tightly over the top of the
glass rod. Before the glass rod is inserted a little strong
sulphuric acid is poured in, and rests on the expanded
bottom of the glass vessel, exposing a large surface of
acid for absorbing the moisture contained in the air in
the vessel. When the instrument is not in use a split
indiarubber stopper i, seen in Fig. 40 resting on the
base of the instrument, is inserted to close up the neck
of the glass vessel, which is contracted at the top, partly
for this purpose, and partly to avoid a too rapid inter-
change of air between the inside and the outside of the
glass vessel when the instrument is in use.
The advantages of this insulating stand are : —
1. The rod can be easily taken out and cleaned. To
clean such a rod hold it by the end, and wash it by
means of a clean brush with soda and warm water to
remove the grease ; then rub it with another brush while
a stream of warm ordinary water flows over it, to remove
the soda ; and, lastly, let a stream of distilled water flow
270 PRACTICAL ELECTRICITY. [Chap. VI.
over it to remove the trace of salt which is dissolved in
ordinary water. The rod should be dried before a fire ; or,
better, by being hung up under a glass shade, or in some
confined space free from dust, in which there is a vessel
containing a little strong sulphuric acid. On no account
dry the glass rod hy rubbing it with a cloth, nor touch it
with the fingers except at the extreme end.
2. The rod may be made of dense flint glass which
insulates well, while the vessel may be made of any kind
of glass that can be easily, and, therefore, cheaply
blown, without reference to its insulating qualities.
3. As the rod is easily taken out, the sulphuric acid
can be put into the vessel without splashing the rod ; or
the old acid, after it has become weak by absorbing
water-vapour, may be emptied out, and fresh acid put in
without fear of dirtying the rod. This it would be
difficult to do, even with another opening in the vessel,
if the rod were immovable.
144. Laws of Surface Leakage, and of Leakage
through the Mass. — The film of dirt and moisture on a
rod acts like an exceedingly thin layer of conducting
matter, therefore for stems equally damp and dirty (and
the cleanest glass stem rapidly becomes damp and dirty
when exposed to the air), the surface resistance or insu-
lation
I
where I is the length, and d the diameter of the stem,
since resistance is directly proportional to the length, and
inversely as the sectional area of the conducting layer.
The stem also conducts through its mass, and its resist'
tance in ohms is
I
9 X
4
where g is the resistance in ohms between the opposite
faces of a cubic unit of the glass or other material, of
Chap. VI.]
LAWS OP LEAKAGE.
271
which the insulating stem is made, I its length, and d its
diameter. If I and c? be in centimetres, g must be the
resistance of a cubic centimetre ; or, if I and d be in
inches, g must be the resistance of a cubic inch.
The approximate values of g in ohms per cubic centi-
metre, for some good insulators, are given in Table
No. Y. The resistance of an insulator increases up to
a certain limit with the time the current is kept on, or
with the time of " electrification" as it is shortly called,
so that the values in the table, which have been obtained
after several minutes' electrification, represent approxi-
mately this maximum value. The resistance of insula-
tors also varies with the temperature, but while the
resistance of conductors increases with elevation of
temperature, the resistance of insulators diminishes with
elevation of temperature.
TABLE No. V.
Approximate Ee-
sistauceinolims
Substance.
Tempera-
ture —
Centigrade.
per cubic centi-
metre after
several minutes'
electrification.
Authority.
Mica ....
20°
84 X 1012
Author.
( Standard adopted
Guttapercha .
24°
450 X 1012
\ by Mr. Latimer
( Clark.
SheU-lac. . .
28°
9,000 X 1012
Author.
Hooper' sVulca- 1
nised India- I
24°
15,000 X 1012
Tests of Cables.
rubber . . J
Ebonite . . .
46^
28,000 X 1012
Author.
Paraffin Wax .
46
34,000 X 1012
?>
The resistance of dense flint glass has not, as far as
the author is aware, been measured at as low a tempera-
ture as 40° C. after a long period of electrification. At
100° C, Mr. Thomas Gray found that it was about
206 X 1012 ohms per cubic centimetre, at GO'^ C. about
1,020 xlOi3j and that it increased very rapidly as the
temperature diminished. Some experiments made by
272 PRACTICAI, ELECTRICITY. [Chap. VI.
the author showed that, after several hours' electrifica-
tion, the resistance per cubic centimetre at ordinary
temperatures had a far greater value than this.
In the above formulae for the surface resistance and
resistance of the mass of a rod, the more I is increased, that
is to say, the longer the stem is made, the larger both the
surface and the mass insulation become ; while, on the
other hand, the larger the value of d, the smaller are both
the surface and the mass insulation, the latter, however,
diminishing much more rapidly than the former, as d is
increased. Consequently, while for a long thin rod of
fairly good insulating material the main loss of electricity
will be over the surface, for a very short thick rod, for a
sheet, in fact, of insulating material (for that is what a
rod ultimately becomes, as it is made shorter and thicker),
the main leakage will be through the material if the elec-
tricity is conveyed to the different parts at each side of
the sheet by means of a piece of tin-foil, stuck on both
sides of the sheet of insulating material, and if sufficient
of the surface of the insulating material near the edges
of the sheet be left uncovered to prevent surface leakage.
{See construction of condensers, § 173, page 318.)
145. Corrugating the Sides of Ebonite Pillars. —
In order to increase the value of I in the case of an in-
sulating stem without making it very tall and weak, it
may be made with corrugations, as shown in Fig. 99.
These rings have not only the advantage that I is in-
creased, but the thin edges may be very easily wiped
with a clean cloth, and the insulation thereby improved.
Further, although these edges may be dirtied if the rod
be touched or taken hold of, the cavities between them
will probably be left clean, and hence a continuous line
of dirt will not be formed from the top to the bottom of
the pillar, as would probably be the case, if the surface
of the pillar were smooth without corrugations.
146. Common Fault made in Constructing Ebonite
Pillars. — A common fault made in constructing insu-
lating stems of ebonite, and which should be most care-
Chap. VI.j COMMON FAULT IN EBONITE PILLARS. 273
fully guarded against, consists in drilling a hole right
through the stem, and then inserting into the top of
this hole the screw which holds on the terminal, and into
the bottom the screw which holds the pillar to the
Fig. 99.
base. This continuous hole makes it impossible by
any amount of cleaning and paraffining of the outside
of the stem to obtain good insulation, for even if the
sides of this hole between the ends of the screws were
quite clean, the length of ebonite surface separating the
ends of the screws would be small compared with the
length of the pillar outside, and so the leakage from
274
PRACTICAL ELECTRICITY.
rChap. VI.
screw to screw inside the ebonite pillar would be greater
than along the outside ; but when in addition the sides
of this hole are, as is frequently the case, dirty, the
insulation of the pillar is immensely diminished by the
hole being bored right through. The hole should, there-
fore, on no account be drilled through; and in the
case of any old apparatus in which this mistake has been
made, the screws should be taken out, and the sides of
the hole carefully cleaned with a small brush, such as
is sold for cleaning glass tubes, using first soda and
warm water, then warm water without soda, and, lastly,
allowing a stream of distilled water
to flow through the hole ; finally,
when the sides of the hole are quite
dry, melted paraffin wax should be
poured in, so that there is a little
Ijlock of paraffin wax filling up the
hole between the ends of the screws.
147. Telegraph Insulators. — In
the case of the earthenware, or
porcelain, insulators used to sup-
port telegraph wires, length of sur-
face, combined with small periphery
of a transverse section, is obtained
by means of the " double cup insu-
lator" (Fig. 100). This form of
insulator, which was originally pro-
posed by Mr. Latimer Clark, has
also the advantage that the inner
surface 2, 2 of the outer cup, as
well as the inner 4, 4, and outer
surface 3, 3 cf the inner cup, are kept tolerably clean
and dry. Before the electricity escaping from the wire,
which is bound in the groove at the upper part of
the insulator, can reach the iron stalk, by means of
which the insulator is attached to the wooden or iron
bracket on the telegraph post, it must leak down the
outside of the outer cup 1, 1, then up the inside of the
Fig. 100.
Chap. VI.] TELEGRAPH INSULATORS. 275
outer cup 2, 2, then down the outside of the inner cup
3, 3, and, lastly, up the inside of the inner cup 4, 4.
The porcelain, or earthenware, cups should, as origi-
nally suggested by the late Mr. Cromwell Yarley, be
moulded separately, and cemented together after they
are baked, in order that a possible flaw in the one may
not be accompanied by a flaw in the other, which would
probably be the case if they were moulded in one and
then baked. The lips of the cups should be shaped as
shown in the figure, for, with this shape, Mr. Varley
found that the drops of water hanging on the lip during,
or after, rain, were simply blown a little way up inside
the cups, instead of being broken and the moisture
scattered all over the inside of the insulator, moistening
all parts.
148. Testing Insulators during Manufacture. — In
order to test the quality of insulators, a hundred of them
are placed, inverted^ so that they can hold water, in a
shallow metal-lined trough, containing sufficient water to
come to within half an inch of their lips, and water
having been poured into both the cups so as to reach to
about the same height, the insulators are left in the water
for at least forty-eight hours, to give time for the water to
soak into any cracks in the earthenware or porcelain. The
metal stalks of all the insulators are fastened together
with copper wire, and the resistance between this copper
wire and the water in the trough, or, what is electrically
the same thing, the metallic lining of the trough, will
measure the parallel resistance to leakage through the
earthenware or porcelain of which the cups are made,
and over the surface of the lips of the cups. To diminish
the surface leakage as much as possible, the lips are
dried, just before the test is made, by large red-hot rollers
being rapidly rolled backwards and forwards over the
troughs along iron rails fastened on the tops of the sides
of the troughs, this operation being performed so quickly
that the lips of the insulators are dried before any appre-
ciable quantity of the water in the trough or in the
276 PRACTICAL ELECTRICITY. [Cliap. VI.
insulator cups is evaporated, and the air in the neigh-
bourhood of the cups thus rendered steamy. Then,
before the lips have had time to cool, and, therefore,
before any fresh moisture can settle on them, the parallel
resistance is measured.
The resistance of one double cup insulator made of
porcelain, and tested in this manner, varies from five
hundred thousand million to four million million ohms,
depending on the size of the cups, and the quality of the
clay of which the cups are made. Taking two million "meg-
ohms" that is two million million ohms, as the average
resistance of each of a batch of 100, the 100 should have
a parallel resistance of twenty thousand megohms. If a
set of 100 are found to have a parallel resistance much
below the other sets of 100 of the same type, it is either
due to faulty drying of the lips, or to the presence of one
or more cracked porcelain cups in the batch, or to one or
more of the porcelain cups having been badly baked.
Under these circumstances a red-hot iron roller should be
again rolled backwards and forwards over the trough,
when, if the same low resistance is again obtained, the
wire should be unwound from the iron stalks, and each
insulator should be tested roughly and quickly^ by touch-
ing the stalk with one of the copper wires connected
with the measuring apparatus, the other wire coming
from the measuring apparatus being still attached to the
metallic lining of the trough. In touching the stalk
with the wire, care must be taken to hold the india-
rubber or guttapercha covering at some little distance
from the end, and the insulating coating must be cut
like a pencil, as shown in Fig. 98, page 267 ; otherwise
the leakage to earth along the outer surface of the in-
sulated wire will be mistaken for leakage through the
porcelain of an insulator. In this way the defective in-
sulator or insulators may be detected and removed from
the batch.
This rough method of picking out defective insulator
may with advantage be employed before the stalks of the
Chap. VI.] TESTING TELEGRAPH INSULATORS. 277
insulators are wired together, and the parallel resistance
of the batch of 100 tested accurately. For supposing one
million megohms were taken as the " specified " or con-
tract minimum resistance of each insulator, then, if ninety-
nine of them happened to be each of them better than
the specified standard, having, say, each three million
megohms, whereas one of them was much below the
standard, and had only, say, twenty thousand megohms,
the parallel resistance of the 100 would be 12,048
megohms. But as this would be more than the specified
resistance of a good hundred, which would be ten thousand
megohms, it follows that, although the batch contained
an insulator having only the yl^th of the resistance of
each of the remaining ninety-nine, the batch would be
allowed to pass if the insulators were only tested in
hundreds, and were not subjected individually to any
test. But such an insulator, which had only the x^o*^
of the resistance of each of the rest, should certainly be
rejected, since, although the defect at present is only a
small one, it is extremely probable that this defect will
go on increasing, so that if it be put up with others
on a telegraph line, more electricity will eventually leak
through this insulator to the ground than will escape
over the surface of all the insulators which support
several miles of the telegraph wire.
149. Measuring High Resistances. — With an or-
dinary Wheatstone's bridge we can test resistances up to
1-11 million ohms, but not above that, consequently resist-
ances of thousands of megohms are usually tested in quite
a different way, by measuring the current that a known
P. D. will send through them. As, however, the gal-
vanometer must be extremely sensitive to enable such
small currents to be measured by means of it, and as the
absolute value of the deflection of such a very delicate
or sensitive galvanometer is liable to vary from day to
day, we do not attempt to calibrate the galvanometer
absolutely in amperes, or rather in millionths of an am-
pere. Further, it is not necessary to know the value in
278
PRACTICAL ELECTRICITY.
[Chap. VI.
volts of the P. D. employed, since, if we compare the
current sent by this P. D. through the unknown resist-
ance with that sent by the same P. D., or by a known
portion of it, through a known resistance, the value of
the unknown resistance can be ascertained.
150. Subdividing a P. D. into Known Fractions.—
The simplest arrangement for obtaining a known fraction
of a P. D. is to cause a steady current, by means of a
battery b (Fig. 101), to flow through a veiy high resist-
ance L M ; then the P. D. between any two points s t,
bears to the P. D. be-
tween any other two
points L M, the ratio
that the resistance q
of the part s t bears to
the resistance p of the
whole L M. The P. D.
between the points l m
^iff« 101. may be employed to
send a current through
the unknown resistance x, and the P. D. between the
points s T, through a known resistance r.
It is not, of course, necessary that both the points
s and T should be distinct from l and m ; one of them,
for example, s, may be the same as l.
151. Constant of a Galvanometer. — If the unknown
resistance x be very large, the galvanometer must be very
sensitive ; hence either the known resistance r must be
also very large, or q must be very small compared with 77,
or, lastly, the galvanometer must be shunted in taking
what is called ^Hhe co'tistant of the galvanometer." If the
resistance l m be very accurately subdivided, then there is
no objection to taking q as small as we like ; indeed, taking
q very small has in such a case an advantage over shunting
the galvanometer, arising from the fact that the smaller q
is, and the higher the resistance of the galvanometer circuit
(the coils of which are attached to the two points s and
t), the more accurately is the iJarallel resistance between
Chap. VI.]
MEASURING HIGH RESISTANCES.
279
s and T equal simply to q. If, on the other hand, the
resistance L m be not very accurately divided, then it is
not advisable to take the points s and t too near together,
since a very small absolute error in the value of q will
make a very large error in the ratio of q to ^j when q is
very small. In that case, shunting the galvanometer is a
better method of diminishing the galvanometer deflection.
Let C and C be the relative strengths of the currents
passing through the galvanometer when, first, the P. D.
between l and m is employed in sending a current
through X with the galvanometer unshunted (Fig. 102),
Fig. 102.
Fig. 103.
and when, second, the P. D. between s and t is sending
a current through r, the galvanometer of resistance ^,
being shunted with a resistance s (Fig. 103), then
q 0
V
8 -\- g
x = '- X - X
q C
sg
r-\-
s + g,
s-\-g
\ 8-\- gl
Generally ~~^~' niay be neglected in comparison with
r, and g in comparison with. x. In which case very
approximately we have
p C s -\-g
^ = 7^0^ ~V ^"-
280 PRACTICAL ELECTRICITY. [Chap. VI
If we have not a large subdivided resistance, l m
(Figs. 102, 103), then we must employ a battery of many
cells in series when sending the current through the high
resistance x, and a small battery, one cell perhaps, when
sending the current through the known resistance r. In
such a case the ratio of the electromotive forces of the
large number of cells to that of the small number will be
approximately proportional to the numbers of cells
employed, but it may be more accurately ascertained by
one of the methods already described (§§ 131, 132, pages
231, 234) for comparing electromotive forces. Let N be
the ratio of the electromotive forces, and let b and b' be
the resistances, in ohms, of the two batteries, then if 0
and C be the relative strengths of the current, as before,
N s 10
X + b + g '
s + 9
c'
• *•
oj = N X — X
0
s V s + g/
- {b + 9).
Or,
as usually b' +
s-\-g
is small compared with r
, and
as b -^ g is also
approximately
X =
small
N X
compared with a;,
C s^-g
0 s
we
have
Example 81. — Using a galvanometer, the deflection
of which is directly proportional to the current passing
through it, and having a resistance of 7,500 ohms, a
deflection of 220 divisions on the scale is produced when
p is 10,000 ohms, and the current is sent through the
unknown resistance. On the other hand, when q is 100
ohms, and the current is sent through a known resistance
of 10,000 ohms, a deflection of 300 scale divisions is
obtained with the galvanometer shunted with 7*508
ohms. What is the value of the unknown resistance 1
Using the complete formula we find that the un
Chap. VI. j VERY DELICATE GALVANOMETERS. 281
known resistance is 1,364,561,591, while the approximate
formula gives as the result 1,363,636,364. For all
practical purposes it would be sufficient to know that the
resistance was 1,364 megohms, which result would be ob-
tained quite as accurately from the second answer as from
the first.
Example 82. — With 100 cells and the unknown .re-
sistance a deflection of 192 scale divisions is obtained,
whereas with one cell and a known resistance of 25,000
ohms in circuit a deflection of 243 scale divisions is pro-
duced when the galvanometer is shunted with the one-
hundredth shunt. What is the value of the unknown
resistance? Aifiswer. — 316 megohms approximately.
Example 83. — If one cell give a deflection of 100
scale divisions when 10,000 ohms are in circuit, and the
galvanometer is shunted with the one-thousandth shunt,
how many cells must be used to test a resistance of
10,000 megohms if a deflection of not less than 50 scale
divisions is to be obtained ?
Answer. — 500 cells approximately.
Example 84. — If one cell give a deflection of 127
scale divisions when 12,000 ohms are in circuit, and the
galvanometer is shunted with the one-thousandth shunt,
through what resistance would one cell give a deflection of
one scale division if the galvanometer were unshunted?
Answer. — 1,524 megohms approximately.
152. Very Delicate Galvanometers.---For measuring
accurately the current that 100 Daniell's cells will send
through, say, 20,000 megohms, which is only the one two-
hundred-millionth part of an ampere, we must employ a
galvanometer which is far more sensitive than anything
that has hitherto been described in this book. To obtain
this high degree of delicacy three conditions must be
fulfilled :—
1. The number of turns of wire on the galvanometer
bobbin must be very large. {See § 217, page 418.)
282 PRACTICAL ELECTRICITY. [Chay. VI.
2. The suspended magnetic needle must be strongly
magnetised.
3. The controlling force must be very weak.
In order to fulfil condition No. 1, and, at the same
time, to keep all the turns of wire close to the suspended
magnet, very fine wire must be used in winding the
bobbin. No. 2 is fulfilled by making the needle of hard
steel; a piece of watch spring heated to redness and
cooled suddenly by being dipped in water answers well.
By the proper adjustment of an auxiliary magnet the
controlling force due to the
earth or other controlling
magnet may be rendered
very weak for any one
position of the suspended
needle of the galvanometer,
but unless the controlling
magnet be very large and
far away it is difficult to
obtain a sufficiently uniform
field for the controlling
Fig. 104. force acting on the sus-
pended magnet to be weak
throughout the whole range of motion of the suspended
magnet. A better plan is to make the suspended ar-
rangement of two magnets N S, N' S' rigidly fastened,
with their poles reversed, to a stifi" vertical wire (Fig.
104). If these two magnets N S, N' S' be of exactly the
same length and strength, and if their poles be in exactly
the same vertical plane, the earth's magnetism will have po
effect on the arrangement, hence it will rest indifferently
in any position about a vertical axis as far as the earth's
attraction is concerned.* But if one of these magnets be
* As it is extremely difficult to fix the magnetic needles to the
vertical wire so that their magnetic axes are in the same vertical
plane, the practical test for the needles being equally strong is not
that the arrangement will rest indifferently in any position when it is
acted on by the earth's magnetism alone, but that the needles place
themselves east and west, since this is the only position in which the
Chap. VI.] Thomson's astatic galvanometers. 283
inside one coil of wire, and if the other be inside another,
and if the current flow in opposite directions round these
coils, '■^ the moment of the deflecting couple"* acting on
the combination will be the sum of the moments of the
couples acting on the two needles separately, and hence
may be made as large as we please. Such an arrangement
is called an " astatic combination " of magnets, and with
it a galvanometer of great delicacy, called an " astatic gal-
vanometer,^^ may be made.
In practice a small directive force is produced partly
by one of the needles being a slightly stronger magnet
than the other, and partly by a controlling magnet M
(Fig. 108) being placed nearer one of the needles than
the other, and so acting more strongly on that one.
153. Thomson's Astatic Galvanometers. — Usually
in Sir William Thomson's astatic galvanometers the
forces acting on the arrangement due to the earth's magnetism balance
one another. Actually the needles place themselves so that their axes
are equally incUned to the east and west line, but the inclination is so
slight that they appear to lie east and west. In Fig. 105 the equilibrium
Fig. 105. Pig. 106.
position is shown, the needles being seen in plan, and their axes, for the
purpose of clearness, being drawn more inclined to one another than
they would be in practice. Fig. 106 shows the arrangement slightly
turned round, when it is seen that equilibrium cannot exist.
* When two equal forces opposite in direction and parallel to one
another, but not in the same line, act on a body, they constitute a
"couple^' whose "mo7nent" is the iwoduct of either force into the
perpendicular distance between them.
284 PRACTICAL ELECTRICITY. [Chap. VI.
mirror is fastened to one of the magnets, and an
aluminium vane to the other, to produce ^^ damping "
or resistance to quick vibrations of the needle, in con-
sequence of which it is rapidly brought to rest when
deflected ; and the mirror- and the vane are attached to
a vertical wire— made, like the vane, of aluminium for the
sake of lightness — suspended by a fibre of unspun silk.
This arrangement, however, has two disadvantages : the
one that, as the mirror and the vane are much larger
than the magnet, the inner windings of the wire in the
coils cannot be brought . close to the little mjignets ; the
other that, in order to allow the reflected ray (see
Fig. 38, page 107) to emerge from the coil when the
mirror is deflected, the hole in the coil must be enlarged
at the front, that is, made trumpet-shaped, which causes
the wire to be still farther removed from the suspended
magnet. A better plan is to dispense with the aluminium
vane and attach the mirror and the magnets to a vertical
strip of mica ss (Fig. 107), as such a strip produces suffi-
cient damping to render the galvanometer dead beat. Fur-
ther, by attaching the mirror o to the part of the vertical
strip that is between the coils, as shown in the figure,
the space inside the coils which is not wound with wire
need only be large enough to allow sufficient clearance
for the free motion of the magnets when they are
deflected, so that the convolutions, of wire can be brought
close to the magnet and the instrument made very
delicate. Also the arrangement enables a larger mirror
to be employed and a brighter image obtained on the^cale.
The astatic combination shown in Fig. 107 consists
of four small magnets m^ in the centre of one pair of
coils, with their marked poles, say, all turned to the
right, and four similar small magnets m, in the centre of
the other coil, with their marked poles all turned to the
left. The strip of mica s s, to which these two sets of
magnets are fastened, hangs by a fibre of unspun silk
from a small hook at the end of a screw, which can be
raised or lowered by turning the nut n. To prevent the
Chap. VI.] MODIFIED THOMSON'S GALVANOMETER.
285
Bcrew also turning and twisting the fibre when the nut n
is turned, there is a small vertical groove cut in the side
of the screw, in which runs a small pin attached to the
framework of the galvanometer.
In order to insert the astatic combination of magnetic
needles in the instrument, two of the coils must be re-
moved. This is much facilitated if the coils be mounted
Fig. 107.
in hollow boxes b b, attached by hinges to the frame-
work of the galvanometer, as seen in Fig. 107, which
shows, two of these boxes containing the coils turned
back so that the interior of the galvanometer may be seen.
To prevent the coils touching the suspension when the
boxes are closed, strips of paraffin wax or guttapercha, F,
are inserted.
All reflecting galvanometers which have not an ad-
justment for centring the fibre should be provided with
two adjustable spirit-levels L L, attached, at right angles
286 PRACTICAL ELECTRICITY. [Chap. VI.
to one another, to the base of the galvanometer. When
tlie instrument is made, the levelling screws, on which
the galvanometer rests, should be adjusted until the sus-
pended needles hang quite freely inside the coils, then
the levels should be adjusted until the bubble of air is
in the middle of each tube. On all future occasions when
the instrument is used, the levelling screws should be
turned round until the bubbles are in the centres of the
tubes, and then we may be sure that the needles are
hanging freely inside the coils. If the whole apparatus
could be made perfectly true, the mere levelling of the
base with an ordinary carpenter's level when the galvano-
meter was about to be used would be sufficient to insure
perfect freedom of the needles ; but if the aluminium wire
be not perfectly straight, or if the coils be not perfectly
symmetrical, from the wire perhaps having bulged, the
mere levelling of the base would not suffice.
154. Importance of the Galvanometer being Well
Insulated. — In many cases when a high resistance has to
be measured it is the resistance between some insulated
body and the earth ; for example, the resistance of the
layer of guttapercha between the copper conductor of
a cable and the water. It is impossible, of course, to
insert the galvanometer between the guttapercha and
the water, hence it must be placed between the battery
and the insulated body. The currents, therefore, that
will pass through the galvanometer will be the sum of
the current that passes through the resistance that we
desire to measure, and the current that will leak to
earth from the terminal of the galvanometer that is
attached to the insulated body, if this terminal be not
well insulated. The value of this leakage current can be
ascertained by disconnecting the galvanometer from the
body whose insulation we desire to test, and testing the
insulation of the galvanometer alone ; but a better plan
is to endeavour to render these leakage currents prac-
tically nought by having all parts of the galvanometer
well insulated, as well as the wire connecting the
Chap. VI.] MODIFIED THOMSON'S GALVANOMETER. 287
Fig. 108.
288 PRACTICAL ELECTRICITY. rChap. "VT.
galvanometer with the insulated body. To insulate the
coils of the galvanometer from the earth the hollow
boxes B B (Fig. 107) in which the coils are held, as well
as the pillars p p, are, in the best galvanometers, made
of ebonite. The ends of the coils should be fastened
to ebonite pillars p p, inside the outer brass case of the
instrument, and the wires employed to connect the
galvanometer with other apparatus can be attached to
the terminals at the top of these pillars either by passing
the wires through openings in the brass case, which
openings may be closed by little doors when the galvano-
meter is not in use, or, better stijl, the flexible wires may
be attached to terminals T T, at the ends of horizontal
stiff brass wires w w, the other ends of which are screwed
into the terminals t t, at the tops of the ebonite pillars
p p, as seen in Fig. 107. These stiff brass wires pass
through holes h h, in the brass cover q, which is shown
removed from the galvanometer in Fig. 108, without
touching it, and by pushing in the ebonite collars e e,
which slide on the wires w w, the holes h h can be closed
up, either when the galvanometer is not in use, or when
it is employed for experiments not requiring the highest
insulation of the terminals. When it is desired to
remove the cover, the wires w w are first unscrewed from
the terminals t i and withdrawn, then the small screws
at the bottom of the cover (Fig. 108), which screw into the
brass lugs at the base of the galvanometer (Fig. 107),
are loosened.
G (Fig. 108) is a window let into the cover for the
light to pass through on its passage to and from the
mirror; s is a screw held against the worm-wheel w by
a spring r, and by turning the handle the controlling
magnet M can be turned round, and the spot of light
brought to the centre of the scale. By raising or lower-
ing M the sensibility of the galvanometer is increased or
diminished.
In some cases the unknown resistance is so large —
when it is, for example, the insulation resistance of a
Chap. VII. I THE COULOMB. 289
short bit of good cable — that even the method of testing
described in § 151, page 279^ is not sensitive enough to
give its value ; in such a case the " leakage method of
measuring resistance " described in § 185, page 344, must
be resorted to.
CHAPTER YII.
QUANTITY AND CAPACITY.
155. Coulomb — 156. Ballistic Galvanometer — 157. Correction for
Damping — 158. Logarithmic Decrement — 159. Determining the
Logarithmic Decrement when the Damping is very Slight —
160. Comparing Quantities of Electricity — 161. Capacity — 162.
Condenser— 163. Capacity of a Condenser is Constant — 164.
Variation of the Capacity of a Condenser with the Area of its
Coatings— 165. Variation of the Capacity of a Condenser with the
Distance between the Coatings — 166. Farad — 167. Charge in
Terms of Capacity — 168. Capacity of a Cylindrical Condenser —
169. Specific Inductive Capacity — 170. Condensers for Large
P. Ds.— 171. Leyden Jar— 172. Battery of Ley den Jars— 173. Con-
structing Condensers of very Large Capacity — 174. Comparing
Capacities — 175. Condensers are Stores of Electric Energy, not
of Electricity — 176. Charge and Discharge Key — 177. Absolute
Measurement of a Capacity — 178. Statical Method of Comparing
Capacities— 179. Measuring Specific Inductive Capacity— 180.
Standard Air Condenser — 181. Every Charged Body is One Coat-
ing of a Condenser — 182. Capacity of a Spherical Condenser — 183.
Condenser Method of Comparing the E. M. Fs. of Current Gene-
rators— 184. Condenser Method of Measuring the Resistance of a
Current Generator — 185. Measuring a Eesistance by the Rate of
Loss of Charge — 186. Rate of Loss of Charge from Leakage
through the Mass depends on the Nature of the Dielectric, and
not on the Shape or Size of the Condenser — 187. Galvanometric
Method of Measuring Resistance by Loss of Charge — 188. Multi-
plying Power of a Shunt used in Measuring a Discharge — 189.
Production of Large Potential Differences — 190. Condensing
Electroscope — 191. Calibrating a Gold-Leaf Electroscope — 192.
Electrophorus — 193. Ebonite Electrophorus arranged to give
Negative Charges — 194. Accumulating Influence Machines— 195.
Thomson's Replenisher— 196. Wimshurst Influence Machine—
197. Dry Piles.
155. Coulomb. — A " coulomb " is the unit of electric
quantity, and it is defined as the quantity of electricity
that flows per second past a cross section of a conductor
conveying an ampere. In the case of a stream of water
T
290 PRACTICAL ELECTRICITy. [Cliap. VU.
through a pipe we can measure the current by putting a
bucket under the end of the pipe, and actually measuring
the number of cubic feet or gallons of water that flow
out per minute, but in the case of an electric current
there is no end to the pipe or conductor, since the
electric circuit is necessarily a closed one, and if we
attempted to cut the wire for the purpose of inserting
some apparatus in order to catch, so to say, the electricity,
we should stop the current. What we have, therefore,
to do in order to measure a quantity of electricity is to
discharge the body containing it through the coil of
a galvanometer, and observe the current produced during
the discharge. This discharge of electricity, and the
current produced by it, last a very short time, and,
further, the current changes in value rapidly during the
discharge. For example, suppose that an insulated con-
ductor containing K coulombs of electricity, and charged
to a potential of V volts, be discharged by being con-
nected with the eround throuorh the coil of a ^alvano-
meter ; then, as the electricity flows out, the potential of
the conductor will fall, hence the P. D. between it and the
ground, and consequently the current, will rapidly grow-
less, until, when the discharge is nearly completed, and
the potential is nearly reduced to that of the earth, the
current will be extremely small. The efiect, therefore,
of sending such a discharge of electricity through a
galvanometer coil is to cause the needle of the galvano-
meter to be suddenly deflected, after which it returns
through the zero position, at which it finally stays at
rest after a few swings. Although the current during
the discharge is rapidly growing less and less, and
although, therefore, the impulses given to the needle
during successive equal short intervals of time during
the discharge become feebler and feebler, it is possible,
when the whole discharge is completed before the needle
begins to move, to sum up the effects of all these impulses,
and so to estimate the number of coulombs of electricity
that pass during the discharge from the instantaneous
Chap. VII] MEASURING QUANTITIES OF ELECTRICITY. 291
deflection or '' elongatiouy* or " throw " of the needle, as it
is sometimes called. The magnitude of this first angular
deflection of the needle k° depends —
1. On K the number of coulombs that pass.
2. On the moment of inertia of the needle and
pointer, or other indicating arrangement.
3. On the moment of the controlling forces, that is, the
forces which resist the needle moving away from the zero
position, and which tend to pull it back to that position.
4. On the moment of the forces that " damp " the
vibrations, that is, the forces, due to air or "7nag7ietic
friction," that simply resist the motion of the needle (see
§ 156, page 294).
5. On the moment of the deflecting forces exerted
on the needle by a given constant current flowing
through the coil.
Increasing either 1 or 5 will increase the magnitude
of the first swing, which, on the other hand, will be
diminished by increasing either 2, 3, or 4. If the
needle be set swinging when no current is flowing, the
quickness of the vibration will depend on the largeness
of 3, and on the smallness of 2 and 4, so that if P be
the "periodic time of vibration " of the needle in seconds,
that is, the number of seconds that interve7ie between the
moment when the needle passes any position and the
moment when it next passes the same position swinging in
the same direction, P will be increased by diminishing 3, or
by increasing 2 or 4. On the other hand, if a° be the
angular deflection produced when a steady current of
A amperes flows through the coil, a° will be increased by
increasing 5, or by diminishing 3, but will be unafiected
by altering 2 or 4.
Taking all these effects into consideration, it can be
shown that, when both k° and a° are small, and when the
damping is very small,
p . k^
= —X Ax 2
292 PRACTICAL ELECTRICITY (Chap. VIL
If a reflecting galvanometer be employed, k° and a°
will necessarily be both small, because, with a scale say
two feet long, put four feet away from the mirror, the
spot of light will be deflected from the centre to the end
of the scale by the mirror turning through an angle of
only 7°. Indeed, with a reflecting galvanometer, as
explained in § 66, page 108, we may, with considerable
accuracy, replace the angular deflections by the number
of divisions on the scale through which the spot of light
is deflected. Let these be k and a respectively, then
P A >fc
K = — X -rt X — very approximately.
In order that we may employ this formula without error
to measure a quantity of electricity directly in coulombs,
it is necessary to employ a " ballistic galvanometer."
156. Ballistic Galvanometer. — In order to employ
an ordinary reflecting galvanometer as a ballistic galvano-
meter, the " air vane " should be removed to diminish
the damping as much as possible, or if the support for
the mirror and the magnets be the air vane as in s s
(Fig. 107), it should be replaced by a vertical aluminium
wire ; and, in addition, the needle should be weighted, as
this not only still further diminishes the damping action,
but makes the vibrations much slower, and so enables
the periodic time P to be accurately determined. Also
this increase in the periodic time tends to prevent the
needle starting before the discharge has been completed,
which is the fundamental condition that must be fulfilled
in order that this formula may be true. A very suitable
form of galvanometer to be used as a ballistic galvano-
meter is shown in Fig. 109, in which r, r are the coils, and
inside which is suspended a bell-shaped magnet, devised by
Messrs. Siemens and Halske, seen in elevation in m, and in
plan in n s, to the left of Fig. 109. By means of an alumi-
nium wire the magnet is attached to a mirror s, and the
whole suspended by a long fibre of unspun silk, hanging
inside a glass tube r. The fibre can be raised or lowered
Chap. VII.]
BALLISTIC GALVANOMETERS.
293
by means of the vertical pin at the top of the tube, and it
can be centred by means of the three horizontal screws
(two only of
which are
seen in the
figure)which
hold in posi-
t i o n the
outer brass
collar cover-
ing the ver-
tical pin.
In the
case of a gal-
vanometer
provided
with a cen-
tring ar-
rangement,
such as is
shown in
Fig. 109, it
is not neces-
sary to have
adjustable
levels, as
seen in Fig.
1 07,because,
when the in-
strument is
constructed,
the base can
be levelled
with an ordi-
nary level,
and the nee-
dle then centred by means of the three adjusting screws
at the top of the tube. On all future occasions when it
294 PRACTICAL ELECTRICITY. [Chap VII.
is desired to use the galvanometer, all that need be done
is to level the base, since when this is done we are sure
that the needle is properly centred.
This galvanometer, as usually constructed, contains a
large copper ball inside the coils, which is shown in
section in K, at the upper right hand of the figure ; but
this ball, which is introduced for the purpose of damping
the vibrations, must, of course, be removed when it is
desired to use the instrument as a ballistic galvanometer.
The copper ball damps by the magnetic friction produced
by the attraction between the moving magnet and the
electric currents induced in the copper by the motion.
When making experiments with a ballistic galvano-
meteVy great care must he taken that the needle is absolutely
at rest when the discharge test is made, otherwise the ap-
preciable momentum, which is possessed by the needle of
large moment of inertia, even when moving slowly, will be
added to, or subtracted from, that given to it by the current,
and will introduce an error. This necessity of waiting
for the undamped needle to come absolutely to rest
makes observations with a ballistic galvanometer most
tedious, and it is well to place, at some convenient spot
outside the galvanometer,- a small independent coil of
wire, in circuit with a cell and a reversing key, by means
of which small impulses may be given to the needle to
stop it when it is swinging.
Example 85. — With a galvanometer, the needle of
which executes 11 complete swings in 6 J seconds 1
Daniell's cell, having an E. M. F. of 1*07 volts, and an
internal resistance of 3 ohms, produces a deflection of
127 scale divisions when there is a resistance of 10,000
ohms in the circuit, excluding the galvanometer which
has a resistance of 7,560, and which is shunted
with the one - thousandth shunt. What number of
coulombs is discharged through the galvanometer when
an instantaneous deflection of 230 scale divisions is
produced 1
Chap. VII.] EXAMPLES. 295
The current producing the steady deflection of 127
scale divisions, is
I 1-07
X amperes,
1'^^^ 3 + 10,000+1^
1,000
or amperes approximately,
10,000,000
^ 6-5 1-07 230 , ,
, . K = X X coulombs
II X X 2 X 10,000,000 127
approximately.
Answer. — 0*01822 microcoulombs approximately.
Example 86. — What alteration could be made in the
galvanometer referred to in the last example other than
altering the coils, so that one-tenth of a microcoulomb
should produce an instantaneous deflection of 100 scale
divisions %
Answer. — Either the sensibility of the galvanometer
must, by slightly approaching the controlling magnet, be
diminished in the ratio of 0*01822 x 100 to 0-1 x 230,
or the needle must be weighted so that the periodic time
is increased in the ratio of 0-1 x 230 to 0-01822 x 100.
Example 87. — Which galvanometer would be the
more sensitive for the measurement of quantity, one
whose needle made 9 complete vibrations in 3 seconds,
and with which a deflection of 200 scale divisions was
produced by 1 Daniell's cell when 10,000 ohms were in
circuit, and the galvanometer was shunted with the one-
hundredth shunt, or one whose needle made 11 vibra-
tions in 7 seconds, and with which a deflection of 85
scale divisions was produced by the same Daniell's cell
when 6,000 ohms were in circuit, and the galvanometer
was shunted with the one- thousandth shunt ?
In order to produce an instantaneous deflection of
100 scale divisions, there will be required with the twc
galvanometers respectively,
2yb PRACTICAL ELECTRICITY. [Chap. VIL
3^ 1__ E 100
97r ^ 2 X 10"0 ^ 10,000 ^ 200'
,7 1 E 100 , ,
and X X — X coulombs,
IItt 2 X 1,000 6,000 85
if E be the E. M. F. in volts of the Daniell's cell,
0-08333 E , 0-06238 E . , ,
or and microcoulombs.
Consequently the sensibility of the second galvanometer
for measuring quantity bears to that of the first the
ratio of 0-08333 to 0-06238, or 1-336 to 1, hence the
second is rather more than one-third more sensitive than
the first.
157. Correction for Damping. — If it is not possible
to remove the vane of a galvanometer so as to diminish the damp-
ing to a very small value, or if it is desired to make very accurate
experiments, in which case the damping, however small, ought to
be allowed for, the following formula should he employed : —
where I is what is known as the " Napierian logarithmic decrement."
This formula is correct when the damping is too great to be en-
tirely neglected, but still not exceedingly large, in which case the
formula is much more complicated.
158. Logarithmic Decrement. — When there is damping,
the amplitude of the oscillations of the needle will grow gradually
less and less, and the ^^ decrement ^^ is the name given to the ratio of
the amplitude of one oscillation to the amplitude of the succeeding one,
and this ratio experiment shows is the same for any two successive
vibrations. The Napierian logarithmic decrement is the logarithm
of this ratio to the base e, or 2-71828, and this again equals the log-
arithm of this ratio to the base 10, divided by the logarithm of
c to the base 10, that is,
log., ratio = ^-^^1111^
0-4343
■•lo ratio
logarithms, but if the value of the fraction be also calculated by
Chap. VII.] LOGARITHMIC DECREMENT. 297
using logarithms, care must be taken to employ log.j^ log.j^ ratio,
that is, to extract the logarithm twice over, because
log. 10 log.e ratio = log.jo log.^, ratio — log.^, 0-4343.
159. Determining the Logarithmic Decrement
when the Damping is Very Slight If the damping is
very slight, it will be very difficult to detect any difference between
the amplitudes of two succeeding vibrations, so that the ratio or
decrement will appear to be unity, and its logarithm nought. The
decrement can, however, be determined a9 follows : — Since the
ratio of the amplitude of the first oscillation to the amplitude of
the second equals the ratio of the amplitude of the second to the
amplitude of the third, &c., each ratio being equal to the decre-
ment, it follows that the ratio of the amplitude of the first oscilla-
tion to the amplitude of the nth oscillation after it, that is the
{n + l)th oscillation, equals the nth power of the decrement, or
generally the ratio of the amplitude of any oscillation to the
amplitude of the nth. oscillation after it equals the nth power of
the decrement.
Consequently,
J amplitude of any oscillation . ,
„ „ the wth „ after it
. , 1_ 2 amplitude of any oscillation
^ „ „ the wth „ after it
Now, although it may be difficult to distinguish the decre-
ment from unity, it is comparatively easy to measure the ratio of
the amplitude of an oscillation to the amplitude of the nth after it,
since n may be taken so large that the ratio differs considerably
from unity.
Example 88. — If, on causing the needle of a galvanometer to
vibrate, the readings on the scale, at which the spot of light stops,
be + 130, - 120, 4- 105, - 97, + 85, «S;c., the + and - indicating
deflections to the opposite side of the zero, what is the value of the
factor 1 + -, the correction for damping ?
Answer. — The amplitude of the first oscillation is 130+ 120,
of the second 120 + 105, of the third 105 -|- 97, &c. Hence, the
decrement equals
250 225 p V i. 1 1 1 1
or > &c., or about 1-111.
225 202
298 PRACTICAL ELECTRICITY, [Chap. VII.
_ 0-0467
"■ 0-4343*
= 0-1052.
Hence, 1+1 = 1-0626.
2i
Example 89, — What amount of damping is allowable so that
the omission of the factor employed to correct for damping shall
not make an error of piore than \ per cent. ?
Answer. — / must equal 0-01, consequently if d be the decre-
ment
log.e d = 0-01,
log.jo d = 001 X 0-4343,
.'. d = 1-010,
or the ratio of the amplitude of one vibration to the amplitud^e of
the next must not exceed 1-01, or the amplitude of one vibration
must not exceed that of the next by more than 1 per cent.
Example 90.-^"With the value of the decrement given in the
last answer, what will be the ratio of the amplitudes of the 1st
and the 15th vibrations ?
^ ^, , amplitude of 1st vibration
Answer.— 0-01 = J^ log.e — ttt, •
„ „ lotn
amplitude of Ist vibration ^.^^
„ „ 15th „
or more simply, thus : —
amplitude of Ist vibration i-oini*
„ „ 15th „
= 1-150.
Example 91. — If the ratio of the amplitude of the 1st vibration
to that of the 21st is 1-2, what is the value of the decrement ?
Answer. — I = J^ log.g 1-2,
.-. 1= 0-00912,
and d=: 1-009;
or we may say at once, i_
.-. d = 1-009.
From this and the previous examples we see that the error in
neglecting the damping will be about ^ per cent, when the ampli-
tude of any vibration exceeds the amplitude of the wth vibration
after it by n per cent, of the latter.
Chap. VII.] COMPARING QUANTITIES OP ELECTRICITY.
299
160. Comparing Quantities of Electricity. — If two
quantities of electricity K and K' coulombs are to be
compared with one another, it is not necessary to deter-
mine P nor a since, if k and k' be the number of divisions
on the scale over which the spot of light swings in the
two cases, we have from the complete formula in § 157,
page 296,
K k
K' ~ k''
The correction for damping has also disappeared,
hence when simply comparing two quantities of elec-
tricity our galvano-
meter may conveni-
ently, and without in
the least complicating
the calculation, have a
certain small amount
of damping.
A simple, conveni-
ent, and cheap reflect-
ing galvanometer, to
be used for the simple
comparison of quanti-
ties of electricity, has
been arranged by Mr.
Mather, and is shown
in Fig. 110. It con-
sists of two coils, cc',
supported in position
by fitting into channels
formed on the base, and a vertical narrow strip of mica,
s s, suspended by a fibre of unspun silk, f, carrying the mir-
ror M, and three sets of magnets, m^, m^, and m3,the first and
third of which form an astatic combination with the middle
set, m^, which is inside the coils : m^ and m^, although not
surrounded with wire, are nevertheless deflected by the
current passing round the adjacent convolutions of the coil
Fig. 110.
300 PRACTICAL ELECTRICITY. [Chap. VH.
in the same direction as m^, which is inside the coil, so
that the magnetic forces acting on all three sets of
magnets conjoin in their effects. The damping arising*
from the resistance of the air to the motion of the
mirror will be sufficient for very accurate capacity experi-
ments, and the strip s s may be replaced by an aluminium
wire. If, however, rather greater damping be desired it
can easily be produced by using the narrow strip of
mica to support the needles and mirror, as in the
galvanometer shown in Fig. 110. The magnets may be
raised or lowered by the pin p, and to avoid torsion
Fig. 111.
being given to the fibre by the head of the pin being
turned round in an unknown way, there is a vertical line
drawn on the pin, and a mark made on the collar in
which this pin slides, and by keeping the line on the pin
always opposite the mark on the collar when the pin is
raised or lowered, all turning of the pin can be avoided.
This contrivance is, of course, cheaper than the simplest
mechanical arrangement for preventing rotation of the
pin when it is raised or lowered.
161. Capacity. — When one conductor is completely
surrounded by another, the " capacity " of the inner one
is the numher of coulombs required to he given to the inner
to produce 1 volt P. D. between the two. For example, the
capacity of A (Fig. Ill), is the number of coulombs on A
when there is 1 volt P. D. between a and b.
The capacity of a conductor, therefore, depends on its
external shape, and on its position relatively to the
Chap. VII, 1 CAPACITY. 301
conductor surrounding it, since, as seen in §§ 66, 67,
page 119, the potential of a conductor relatively to
another can be varied without altering the quantity of
electricity on the former, by varying either its external
shape or its position relatively to the latter. If a
metallic plate a (Fig, 112) be surrounded with a flat
metallic box b, the top and bottom of the box being
parallel to A, and veri/ near A, then the capacity of A will
be very large, since it will require a very large charge of
Fig. 112.
electricity to be given to A in order to raise the P. D.
between a and b to 1 volt.
162. Condenser. — An arrangement of conductors such
as is shown in the last figure is called a " condenser" so
that a condenser may be defined as two conductors
separated hy an insulator, and so placed 7'elatively to
one another that the capacity of the arrangement is large
compared with the size of tlie conductors.
A condenser having a large caJDacity does not, of
course, mean that it would hold a large charge without
its insulation breaking down, but that it would hold a
large charge for the P. D. between its coatings. As far
as power to hold a charge from the non-breaking down
of the insulation is concerned, a condenser of small
capacity may be able to hold a larger charge than a
condenser of much larger capacity.
If A (Fig. 112) be charged with positive electricity,
there will be a charge of negative electricity on the
inside of b, whereas if a's charge be negative, then the
charge on the inside of b will be positive. We have
further seen (§ 60, page 113) that the quantity of elec-
tricity on A is exactly equal in amount to the charge of
the opposite kind of electricity on the inside of B. We
302
PRACTICAL ELECTRICITY.
[Chap. VII.
may, therefore, define the capacity of the condenser either
as the number of coulombs necessary to be given to a, or
the number of coulombs on the inner surface of B when tJie
P. D. between them is 1 volt.
If we desire to make a condenser with a very large
capacity, we may either make the plates very large, or
the distance between them very small. There are
Fig. llo.
obviously practical difficulties in making the distance
separating the plates very small, as the insulation is
liable to be insufficient, either from particles of dust
passing rapidly backwards and forwards between the
charged plates, and so discharging them, or from actual
sparks passing when the P. D. between the plates is
high. On the other hand, if the plate a and the box b
Fig. 114.
(Fig. 112) be very large in area the apparatus becomes
cumbersome. This difficulty, however, may be overcome
by making both A and B consist of a series of plates
(shown in section in Fig. 1 1 3), and a condenser is usually
symbolically represented in this way, or, still more
simply, by two lines drawn parallel to one another, as in
Fig. 114, and the sets of plates, A and b, are called the
" coatings " of the condenser.
163. Capacity of a Condenser is Constant.— By
charging a condenser with different P. Ds., and measuring
with a galvanometer the quantity of electricity that
Cliap. VII. ] CONDENSERS. 303
enters one of tlie coatings, or the quantity that leaves
this coating when the condenser is discharged, it can be
experimentally proved that this quantity is directly pro-
portional to the P. D. The capacity of a condenser may,
therefore, be defined as the ratio of the number oj
coulombs in one coating to the P. D. in volts between the
coatings^ this ratio being a constant for a given condenser.
Unless the galvanometer employed be very sensitive,
it is better when making the experiment just referred to,
for testing the constancy of the capacity of a condenser,
to use a condenser of large capacity of the type described
in§ 173, page 317.
164. Variation of the Capacity of a Condenser with
the Area of its Coatings. — That the capacity of a con-
denser is directly proportional to the effective area of either
of the coatings hardly needs proof, because a condenser
with coatings of large area may be regarded as being
made up of two or more smaller condensers, such that
the sum of the areas of one set of coatings of the smaller
condensers is equal to the area of one of the coatings of
the larger, the distance between the coatings in the large
condenser and in each of the smaller ones being the
same, and it is clear that the capacity of the set of
smaller condensers is the sum of their capacities.
165. Variation of the Capacity of a Condenser with
the Distance between the Coatings. — If we had a con-
denser of large capacity, and the distance between the
coatings of which could be varied at will, an examination
of the variation of the capacity, with the distance between
the coatings, might be made by fixing the coatings at
various distances from one another, and measuring the
number of coulombs, or the fraction of a coulomb, required
to charge the condenser in the different cases with the
same P. D. But practically it is found that any condenser,
the size of whose coatings is not so large but that the
distance between them can be conveniently adjusted, has
so small a capacity that when charged with even a large
battery of galvanic cells in series, its charge cannot be
304 PRACTICAL ELECTRICITY. [Chap. VIL
measured with even a very delicate galvanometer. Hence
we are compelled to use some statical method for in-
vestigating the variation of the capacity of a condenser
with the distance between its coatings. One plan would-
be to give the condenser a charge, and then, on varying
the distance between the coatings without discharging it,
to measure the variation of P. D* between the coatings by
means of a suitable electrometer. From this the variation
of the capacity could be at onee determined, since, with
a constant charge in the condenser, the capacity must
be inversely proportional to the P. D. between the
coatings.
The following method, devised by the author, however,
enables us to ascertain the law of variation of the capacity
with the distance between the coatings, without making
measurements either of the various distances between the
coatings, or of the various P. Ds. corresponding with
these distances, bb, b'b', Fig. 115, are wooden boards
(one of which b' b' in the figure is shown removed from the
apparatus, in order that the interior may be seen) with
their surfaces opposed to one another, carefully planed so
as to be parallel, and coated with tinfoil, so as to make
them conducting. These surfaces together form the
outer coating of a condenser corresponding with b
(Fig. 112). The inner coating consists of the two sheets
of tinfoil, T T, t' t', which are parallel to the surfaces of
B b and b' b'. This tinfoil is stuck on thin cloth to give
it strength, as it has to roll over the small rollers r r',
when the rod n, to which one of the edges of each of the
sheets of tinfoil is attached, is pulled down by the thin
silk cord c c, or when, on this cord being slackened, the
weight w w, to which the opposite edges of the two sheets
of tinfoil are attached, pulls t t and t' t' down, and the
rod n up. The rollers r r', which are made of steel, are
only about one-tenth of an inch thick, and are placed
close together, so that the surface of the tinfoil wrapped
round them may be as small as possible, and so that
there may be no inductive action between the tinfoil on
Chap. VII. J
CAPACITY OF A CONDENSER.
305
the vertical wooden boards and the inner surfaces of the
sheets t t and t' t'. The rollers are pointed at their
1(1,*
I s
ends, where they are supported by the brass pieces hh,
which are firmly cemented to the tops of the glass rods
G g'. The two sheets of tinfoil are, therefore, insulated
306 PRACTICAL ELECTRICITY. TChap. VIL
from the ground. To keep the glass rods dry they are
each surrounded with a tube f f, inside which is placed
dry flannel which absorbs moisture. The tubes are
hinged down their sides, so that they can easily be opened
and removed, and in the figure the one belonging to the
rod g' has been removed. Swaying of the weight w w side-
ways, as well as side attraction of the suspended sheets
of tinfoil T T, t' t', are prevented by the weight being
guided by the cord c c passing through it.
The boards b b and b' b', which are, as seen in the
figure, strongly stayed at the back to prevent warping,
can be made to recede from one another by pushing in
the wedge w w, by means of the screw s, or to approach
one another by turning the screw in the opposite direction,
when the wedge is withdrawn, and a spring pressing
against each plate pushes them together. In addition to
the horizontal boards H h', carrying b b and b' b', being
always pressed by these springs against the side of the
wedge to MJ, a pin on the underside of each board slides in
a groove, the groove g' g seen in the figure being that in
which the pin attached to h' slides, b b and b' b', there-
fore, move parallel to themselves, so that in all positions
the opposed surfaces are parallel. The cord c c first
passes under a little pulley p attached to the base of the
instrument, then under a second pulley p, moving with
the wedge, and its end is attached to the pin q (the wedge
in the figure being cut away to show the pulleys). Hence
on turning the screw s, so as to push in the wedge and
separate b b and b' b', the cord c c is slackened, and
consequently the rod n rises, and the weight w w descends,
causing the area of the surface of the tinfoil t t and t' t'
opposed to B B and b' b' to increase, and by selecting a
proper angle for the wedge w w, and a proper pitch for the
screw, the area of the two surfaces of the tinfoil t t and
t't' can be made to increase, so as to be exactly pro-
portional to the distance separating them from the
surfaces of b b and b' b'.
Under these conditions, if the inner coating of th©
Chap. Vn.] THE FARAD. 307
condenser be connected with the gold-leaves of an electro-
scope, and the outer coating of the condenser be connected
with the outside of the electroscope, and if a potential
diflference be set up between the coatings, it will be found
that no alteration of the divergence of the gold-leaves
will be produced by approaching or separating B b and
b' b'. Now the quantity of electricity on the outer sur-
faces of T T and t't' is a constant, since there is no
electricity inside a conductor (§ 64, page 118). Conse-
quently this experiment tells us that if the ratio of the
area of the inner coating to the distance between the
coatings is kept constant, the capacity of the condenser is
constant. But we have seen (§ 1 64, page 303) that the
capacity of a condenser is directly proportional to the
effective area of either of the coatings, hence it fol-
lows that the capacity of a condenser with plane parallel
plates is inversely proportional to the distance between the
coatings.
166. Farad. — A ^^/arad" is the unit of capacity,
and a condenser has a capacity of one farad when a P. D.
of 1 volt between its two sets of plates charges each of
them with 1 coulomb.
If A be the area in square centimetres of the entire
surface of either of the two sets of opposed parallel
plates of an air condenser, and t be the distance in centi-
metres separating them, and if F be the capacity of the
condenser in farads,
F= "^
M31 X 1013 X t
If A be reckoned in square inches, and t in inches,
A
F =
4452 X 1012 X t
A farad is rather a large unit of capacity for ordinary
purposes, hence, one-millionth of a farad, or a " micro-
farad" is more commonly employed. If M be the
308 PRACTICAL ELECTRICITY. [Chap. VII.
capacity in microfarads of the air condenser, and A and
t be in square centimetres and centimetres respectively,
M= ;
M31 X 107 X t
whereas, if A and t be in square inches and inches re-
spectively,
M=
4-452 X 106 X «
In order that the preceding formulae may be strictly
correct, the linear dimensions of the plates must be largo
compared with the distance between them. It can,
however, be made rigorously true even when this is not
the case if a guard-ring, described in § 44, page 89, be
employed with one of the plates, and be at the same
potential as this plate. In that case A is the area of
the smaller plate, not including the area of the guard -ring,
and F, or M, is the capacity of this plate, not including
the capacity of the guard-ring itself.
167. Charge in Terms of Capacity. — If K be the
charge in coulombs in an air condenser, having a
capacity of F farads, when there is a P. D. between the
coatings of V volts, it follows from the definition of
capacity, that
K = F X V,
also if M be the capacity in microfarads that
^ M X V
10«
les. Capacity of a Cylindrical Condenser. — If the
two coatings of an air condenser consist of two concentric cylinders
A B, c D (Fig. 116), of length I centimetres, and of radii or diameters,
R and r respectively, the capacity F in farads
2-413 I
X
1013 log.ioR-log.io»-
■p
As log.jo R — log.^or equals log.jo — , it is ohvious that it
Chap. VII.] CAPACITY OF A CYLINDRICAL CONDENSER. 309
is quite immaterial what units of length are employed in measur-
ing R and r, provided that the same unit is employed in each
case.
If M be the capacity in microfarads,
Ti/r 2-413 I
107 log.ioR— log.io**
A common example of a condenser having its coatings con-
centric cylinders is a submarine
cable {see Fig. 98, § 140, page
267), the outer coating being the
water or the iron sheathing in
contact with the insulating core,
and the inner coating, the sur-
face of the copper conductor.
Consequently, if R be the radius Fig. 116.
of the core, and r the radius of
the conductor, and if u be the length of the cable in knots, the
capacity in microfarads
^_ 2-413 X 2029 X 91-44
107 log.ioR— log.jo**
4-476 n
102 log.jo R— log.io r
169. Specific Inductive Capacity. — The capacity of
a condenser can be still further increased by using, in-
stead of air for the insulator, glass, guttapercha, india-
rubber, paraffin oil, or some other solid or liquid insulator.
If K be the number of coulombs of positive electricity
required to be given to A, and of negative electricity to
B, so as to produce 1 volt P. D. between them when they
are separated by air, then if the air be replaced by some
other substance, and no other change be made in the
condenser, the number of coulombs now required to pro-
duce 1 volt P. D. between a and b, will be
K X " tlie specific inductive capacity."
Hence the specific; inductive capacity of a substance is
the ratio of the capacity of a condenser wJien its plates
are separated hy this substance to the capacity of the
same condenser when its plates are separated by air.
The following table gives a list of the specific inductive
310
PRACTICAL ELECTRICIIY.
[Chap. VII.
capacities of some important substances as determined
by various experimenters, whose names are given in the
third column : —
TABLE No. YI.
Specific Inductive Capacity.
Subst mce.
Specific Inductive
Capacity.
Authority.
Vacuum, air at about O'OOl
miUiinetre pressure . .
j 0-94 about.
Author.
Vacuum, air at about 5 milli-
\ 0-9985
Author.
metres' pressure . . .
1 0-99941
Boltzmann.
Hydrogen at about 760 milli-
0-9997
Boltzmann.
metres' pressure . . .
\ 0-9998
Author.
Air at about 760 millimetres'
i^
Taken as the
pressure
standard.
Carbonic Dioxide at about
1-000356
Boltzmann.
760 millimetres' pressure .
1-0008
Author.
O&efiant Gas at about 760
millimetres' pressure . .
1-000722
Boltzmann.
Sulpbur Dioxide at about
760 millimetres' pressure .
J 1-0037
Author.
n-92
SchiUer.
1-96
Wiillner.
Paraffin Wax, Clear . . .
\ 1-977
Gibson and Bar-
clay. ,
12-32
Boltzmann.
Paraffin Wax, Milky . . .
2-47
Schiller.
Indiarubber, Pure ....
2-34
Schiller.
„ „ Vulcanised. .
2-94
Schiller.
Resin
2-55
Boltzmann.
(2-66
Wiillner.
Ebonite
2-76
SchiUer.
(3-15
Boltzmann.
Sulphur
1 2-88 to 3-21
13-84
WiiUner.
Boltzmann.
Shell-lac
2-95 to 3-73
WiiUner.
Guttapercha
4-2
Mica
5
Flint Glass, Very Hght . .
6-57
>j
„ „ Light . . .
6-85
„ „ Dense . . .
7-4
'J. Hopkinson.
„ „ Double extra
10-1
dense
/
Chap. VII.J SPECIFIC INDUCTIVE CAPACITY. 311
Not merely is the capacity of a condenser increased
by using, say glass instead of air, as the " dielectric " or
insulating material through which the induction takes
place, but the resistance to loss of charge by sparking is
immensely increased ', hence, with a glass condenser far
greater P. Ds. can be used than with an air condenser of
the same size. The resistance to sparking does not de-
pend on the insulating quality of the substance, hut on
its rigidity and the resistance it in consequence op-
poses to rupture.
If, instead of air, a substance having a specific induc-
tive capacity i be employed, in a condenser made of
parallel plates.
¥ = i X
and M = i X
A
M31 X 1013 X t
M31 X 107 X <
if A and t are reckoned in square centimetres and centi-
metres respectively ; and
F = i X
A
4-452 X 1012 X t
and M = i X
4-452 X 106 X «
if A and t are reckoned in square inches and inches re-
spectively.
Similarly the logarithmic formulae given in § 168,
page 308, for the capacity of a cylindrical condenser,
must be multiplied by i, the specific inductive capacity of
the dielectric when this is paraffin wax, glass, &c., or
when, as in the case of a submarine cable, guttapercha or
indiarubber fills up the space between the two con-
ductors.
Example 92. — If the distance between the plates in
an air condenser be 1 millimetre, what must be the area
312 PRACTICAL ELECTRICITY. [Chap. VIL
of each set of plates in order that the capacity may be 1
microfarad 1 Answer. — About 1,131,000 sq. cent.
Example 93. — How many plates about 1 foot square
would be necessary to produce the area required in the
last answer, and what would be the exact size of each
plate 1
If we assume that the plates were each 1 square foot,
then, since the area on both sides of each plate is utilised,
it follows that the number of plates required would be
-~---f-— or 608-7. We could, therefore, either use 608
l,85o'02
plates, each a little larger than 1 square foot, or 609
plates, each a little smaller. The latter will be nearer in
size to the square foot, and using this number, it is easy
to calculate that each plate must be 0*9994 square feet,
or 11*99 inches square. For the other coating b (Fig.
113, page 302), there must be, of course, 610 plates, since
one surface of each of the outer plates of B will have no
action as a condenser.
Example 94. — If the insulating material in a condenser
be paraffined paper, and if we assume that the specific
inductive capacity of the paraffined paper is the same as
that of paraffin wax, 1*977, what must be the thickness of
the paper in order that the condenser may have one-third
of a microfarad capacity when the area of each set of
plates is 205 square feet? Answer. — 0*03933 of an inch.
Example 95. — A cylindrical glass jar one-tenth of an
inch thick, and 3 inches in diameter, is coated inside
and outside with tinfoil on the bottom, and on the sides
for a height of 3 inches. If the glass be extra dense
flint, what must be the P. D. between the tinfoil coat-
ings so that the charge may be one-millionth of a coulomb 1
The glass being very thin, the formulae for a condenser
formed of plane parallel plates may be used. The area
TT X 32
of tinfoil at the bottom is — - — sq. inches, that on the
Chap. VILJ CONDENSERS FOR LARGE P. Da 313
sides TT X 3 X 3 sq. inches. If, therefore, V be the un-
known P. D. in volts,
'^Al' + ^ X 3 X 3
1 4
106 "^ 4-452 X 1012 X ^ •
. •. V = 1247 Answer.— 124:7 volts.
Example 96. — What is the capacity of the glass con-
denser referred to in the last question f
If F be the capacity in farads,
F= ^_.
106 X 1,247
hence the capacity is 0-0008021 microfarads.
Example 97. — The diameter of the copper conductor of the
Direct United States cable being 0'16 of an inch, the diameter of
the guttapercha core 0-446 of an inch, and its length 2,443 knots,
what is its capacity ?
From the formulai in § 168, page 309, we have
102 446
'°^- lio
= 1031. Answer. — 1031 microfarads.
The actual capacity determined by experiment is 1000-4 micro-
farads.
170. Condensers for Large P. Ds.— The charge in a
condenser, K coulombs, equals, as we have already seen,
F X V,
hence this charge can be made great by making one or
other, or both of the factors, F and V large. For experi-
ments with the old form of '^/rictional electrical machines "
or with the more modern form of " influence machines "
(see§ 196, page 371), it is Y that is always made large,
whereas when galvanic batteries are used as the source of
the P. D., it is 'F that is usually made large. In the
recent experiments, however, made by Drs. De La Rue
314
PRACTICAL ELECTRICITY.
[Chap, VII.
charged with
large P. D., and
condenser takes
and Hugo Muller, with their large silver chloride battery,
consisting of some 20,000 cells, the condensers have been
made to stand the high P. D. produced by this battery as
well as to have a large capacity. When thousands of
volts are to be employed, a large resistance to sparking is
therefore quite as important as high specific inductive
capacity, and, as already stated, requires that the dielectric
should be rigid. (See the note to § 192, page 358.)
171. Leyden Jar. — Some kind of glass is usually
employed in. the construction of condensers that are to be
a very
the
the
form of a '^Leyden
jar" a type of which
is seen in Fig. 117.
The name is derived
from the town of
Leyden, at which the
property of electric
capacity was accident-
ally discovered in
1746, by Musschen-
broek, and his pupil
Cuneus. Desiring to
collect the supposed
electric fluid, they used a bottle partly filled with water,
into which dipped a nail, passing through the cork, to carry
the fluid from the electric machine to the water, and on
Cuneus touching the nail with one hand, the bottle being
held in the other, he received a shock.
In the ordinary Leyden jar, such as is seen in Fig.
117, the tin coatings are sheets of tinfoil, one pasted
inside the jar, and the other outside. Electric connec-
tion is made with the inside coating either by a metal
rod or rods resting on the bottom, or more commonly,
by a chain or a flexible bit of wire hanging from a
brass rod, which, in this case, is supported by a wooden
rig. 117.
Chap. VIII LEYDEN JAR. 315
cover to the jar to which the rod is fixed. But such a
Leyden jar, even when the surface of the glass, which is
not covered with tinfoil, is coated with shell-lac or other
varnish, has but a poor insulation in damp weather, and
requires the glass to be constantly held in front of the
fire to be dried. For with the wooden cover in contact
with both the metal rod and with the edge of the jar,
in accordance with the unscientific form of construction
usually adopted, the interior of the glass helps but little
towards holding the charge, seeing that if the outside of
the wooden cover and of the jar be dirty and moist, there
is a direct road for the electricity to leak from the rod to
the tinfoil outside, without passing at all over the glass on
the interior. Hence, that portion of the glass which it
is most easy to keep dry and clean, is rendered useless by
the presence of the wooden cover in contact with the rod.
On this account the form of Leyden jar shown in Fig.
118, and originally employed by Sir William Thomson,
is much to be prefen-ed. The outer coating consists of
tinfoil T T, as in the ordinary Leyden jar, but the inte-
rior is formed of strong sulphuric acid ss, into which
dips a leaden rod L, expanded at the lower part into a
sort of foot so as to stand firmly on the bottom of the
glass jar. Both rod and foot are made of lead so as not
to be acted upon by the acid, but the upper part i of the
rod, which does not dip into the acid, may be conve-
niently made of iron, being less liable to bend than lead.
The mouth of the jar is partially closed with a wooden
cover w, to keep out dust, and retard a too rapid inter-
change of the air between the inside and outside, which
would prevent the sulphuric acid being able to keep the
interior surface of the glass dry. A cork c, sliding on
the rod i, is pressed down when the jar is not in use,
but is raised up to prevent electric contact between
the rod and the cover w w, when the jar is to be
charged.
In Fig. 118 there is seen carried by the iron rod a
metallic cone. This may be used for making experiments
316
PRACTICAL ELECTRICITY.
rOhap. VII.
in density with the proof plane (see § 63, page 118),
and the advantage of attaching the charged cone, or
other conductor (the distribution of density over whose
surface we desire to measure), to another conduc-
tor of large capacity, is that the amount of electricity
removed by the proof plane, each time we touch the
surface of the cone, does not sensibly diminish the poten-
tial or the total charge pos-
sessed by the cone. Without
the use of the Ley den jar,
the effect of touching any
point A on the cone with the
proof plane, and removing
the proof plane, is not merely
to remove the amount of
electricity that was on the
surface of the cone touched
by the proof plane, but to
slightly diminish the density
of every other part of the
surface of the cone, since
electricity has to flow from
the rest of the body to re-
charge the part touched by
the proof plane. Hence, if
the cone be first charged to
Fig. 118. a given potential, and then
the relative densities at any
points A and B be determined by touching them succes-
sively with the proof plane, slightly different results will
be obtained, according to the order in which these two
points are touched. The use of a well-insulated Leyden
jar removes the difliculty, which may also, to a certain
extent, be overcome by first touching A, and measuring
the charge g^, taken away by the proof plane, then
touching B, and measuring the charge q^^ removed,
and thirdly, touching a again, and measuring the
charge ^g, removed by the proof plane on touching a a
Chap. VII.] CONDENSERS OF VERY LARGE CAPACITY.
317
second time, because the density at b will be to the
density at a approximately, as
A glass jar, with a contracted neck, as shown in Fig.
119, would have a much higher insulation as long as the.
interior of the neck was clean, but there would be
greater difficulty in introducing the
acid without splashing the neck, and
in cleaning the inside of the neck
when it became dirty, even if we took
out the metal rod which fits into a
tubulure at the bottom of the vessel,
as does the glass rod in the insulating
stand, Fig. 40, page 112.
172. Battery of Leyden Jars.—
If a greater capacity is desired than
can be obtained with one such Ley-
den jar, when the glass is made as
thin and as large as is practicable,
then a " battery of Leyden jars^^ that ^
is, a number of sulphuric acid Leyden
jars in parallel, should be employed. Fig. 119.
173. Constructing Condensers of
Very Large Capacity. — When a very large capacity is
required the dielectric employed consists usually of sheets
of loafer or of mica, which have been soaked in melted
paraffin wax or in a solution of shell-lac in alcohol.
The sheets of tin-foil are shaped as shown in a
(Fig. 120), one corner being cut off, and the sheets of
insulating material h are made about two inches wider
and two inches longer, and have two corners cut off. On
a sheet of insulating material there is first laid a sheet
of tinfoil, as in c, then a sheet of insulating material is
laid on the top, then a second sheet of tinfoil with its
uncut corner turning the other way, and so on, so that
finally there are a number of alternate sheets of tinfoil
with their corners projecting over the sheets of insulating
318 PRACTICAL ELECTRICITY. [Chap. VII.
material to the right, and the other set of alternate sheets
of tinfoil, with their uncut corners projecting over to the
left. Each of the exposed sets of corners is soldered
together, and forms an electrode or terminal of the
condenser.
When paraffined paper is employed as the insulating
material, the paper is first very carefully examined by
holding it, sheet by sheet, up to the light, so that the
existence of any small holes may be detected, and any
sheet possessing such holes is discarded. The good
sheets are then placed in a bath of melted paraffin wax
/ 1
/
Tin Foil 1
InsulcLtmfi
Material
/
/
Tin FoO
\
a
7j
c
Fig. 120.
warmed by steam to about 110°C., or a little above the
boiling point, so that all water may be driven ofi'. On a
horizontal slab of cast iron, also warmed by steam to
about the same temperature, the sheets of paraffined paper
and tinfoil are laid in the way just described, the sheets
being carefully smoothed with a flat strip of wood as
they are laid on. Two sheets of paper are placed be-
tween each pair of sheets of tinfoil to avoid the possi-
bility of a hole in the paper causing leakage, it being, of
course, most improbable, even if there were a minute
hole in each sheet, that the holes would come exactly
opposite one another. After the condenser has been
built up in this way it is placed between two warm metal
plates, and pressed with a weight of about eight cwts.
while it is cooling, in order that the surplus paraffin wax
may be squeezed out and the whole consolidated.
Chap. VII.] COMPARING CAPACITIES. 319
To avoid the paraffin wax being wasted, it is desirable
to have a kind of gutter all round the cast iron plate, on
which the condenser is built up, for the paraffin wax to
run into.
It is not desirable to use the paraffin wax in the baths
more than once, since even when the temperature is not
raised more than about 110° C. or 120° C, slight decom-
position of the wax may occur, which diminishes its high
specific resistance. The paraffin employed for making
condensers is highly purified, and the residue in the baths
is sold to be used for making candles.
174. Comparing Capacities. — The capacities of two
condensers can be easily compared by successively
charging each condenser with the same P. D., and ob-
serving, by means of a suitable galvanometer, the
amounts of electricity that rush into the condenser to
charge them, or by charging them with the same P. D.,
and then dischargiug them successively through a suit-
able galvanometer, the instantaneous deflection produced
in either case being directly proportional to the capacity.
If the condensers difier much in capacity, so that
when the galvanometer is properly adjusted and a suit-
able P. D. selected to obtain a convenient deflection on
the galvanometer with the smaller condenser, the deflec-
tion obtained with the larger would be much too great,
or conversely if the sensibility of the galvanometer were
arranged, and the P. D. selected with reference to the
larger condenser, the deflection obtained with the smaller
condenser would be much too small ; hence, in order to
make the comparison of the capacities, either the galvano-
meter must have difierent sensibilities, or the P. D. em-
ployed must be diSerent in the two cases.
The only easy way of altering the sensibility of a gal-
vanometer by a definite amount is by shunting it, and even
this method, as was first pointed out by Mr. Latimer
Clark, introduces a certain vagueness when we are deal-
ing with instantaneous deflections and " transient cur-
rents" or currents only lasting for a very short time. (See
320
PRACTICAL ELECTRICITY.
[Chap. VII.
§ 188, page 349.) Hence, it is better to use different
P. Ds. in the two cases, and the simplest method of
obtaining two P. Ds, of a known ratio to one another
is that described in § 150, page 278.
Let F and F' be the capacities of the two condensers,
V and V the P. Ds. employed in charging them, and k
and k' the instantaneous deflections produced either on
charging or on discharging, then
F
F'
175. Charge and Discharge Key. — If it be merely
desired to observe the instantaneous deflection on charg-
ing a condenser, any simple key for closing the circuit
v; k
Y ^ k'
Fig. 121.
may be employed, but if we desire to observe the dis-
charge immediately after removing the battery, and
therefore, before the condenser has lost any of its charge
by leakage from one coating to the other, some special
form of key must be employed, and that shown in Fig.
121 will be found convenient, and has very high insula-
tion. If joined up as shown in this figure, it will be
seen that, on depressing the lever l, contact will be
Chap. VII.] CHARGE AND DISCHARGE KEY. 321
made between the lever and the lower stop s^, while
that between l and the upper stop s^ will be broken.
This will enable the battery b to charge the condenser c
without deflecting the galvanometer g. If, now, the
pressure on the bent lever l be withdrawn, ifc will fly up,
breaking the contact at s^, and so disconnecting the
battery^ while immediately afterwards the contact at Sg
will be made and the condenser discharged through the
galvanometer.
If the key be joined up as shown in Fig. 122, the
galvanometer will measure the charge put into the con-
Fig. 122.
denser on depressing the key, but not the discharge that
will take place on liberating the key. If the insulation
of the condenser be slightly defective, so that there. is
a small leakage from one coating to the other, the swing
of the galvanometer needle on charging the condenser
(Fig. 122) will be larger than it would be were there no
leakage, while, on the other hand, the swing on discharg-
ing will be smaller ; the mean of the two swings may be
taken as a measure of the true charge of the condenser,
independently of the leakage, if the efiect due to the
leakage is small.
When the apparatus is arranged as in Fig. 123, both
the charge and discharge will be measured, producing
deflections on opposite sides of the zero, and therefore
Y
322 PRACTICAL ELECTRICITY. [Chap. VIL
producing practically no effect at all, if made to follow
one another fairly rapidly. The effect of either on the
galvanometer can be prevented by . short-circuiting it
during either the charge or discharge by means of the
short-circuit plug P.
176. Condensers are Stores of Electric Energy, not
of Electricity. — If a suitable galvanometer be inserted
in each of the wires connecting the two coatings of the
condenser c with the two ends of the battery b (Fig. 124),
it will be found on completing the circuit by closing a key
Fig. 123.
at K, that the first swings on the two galvanometers are
such as indicate equal quantities of electricity passing
through them. And if when the condenser is charged
the battery be removed, and the condenser be discharged
by connecting together the wires p and Q coming from
the galvanometer, then the first swings of the galvano-
meter needles will again be such as to indicate that equal
quantities of electricity pass through them, but in this
case in the opposite direction to that in which the elec-
tricity passed during the charge. Hence, both on charg-
ing and on discharging a condenser as 7nwch electricity
passes into one coating as passes out of the other, and
there is no storing, or accumulating, of electricity. In
fact, as far as the galvanometer deflections during the
Chap. VIL] CONDENSERS STORE ELECTRIC ENERGY. 323
charge show, we could not say whether there was a con-
denser at c or a resistance, the value of which was, from
some cause, rapidly increased, to practically infinity, on
completing the circuit. The sudden deflections, however,
produced on the galvanometer when the wires p and Q
are joined together after removing the battery, could not
be produced if c were a resistance, since no alteration
of the value of a resistance can, by itself, and without
any current generator, produce a current. When the
condenser has a large capacity, and when the P. D. em-
ployed in charging it is large, the current obtained on
Fig. 124.
discharging it may produce very powerful effects. Hence,
we are led to conclude that, although a charged condenser
contains no store of electricity, it contains a store of electric
energy, and it can be shown that, if the capacity of the
condenser be F farads, and if it be charged with a P. D.
of V volts, the store of electric energy, or the work this
store can do when the condenser is discharged, equals
F X V2
2-712
foot lbs.
Example 98. — How many times per second would a
condenser of 10 microfarads have to be charged with
86 volts, and discharged so that it would give out about
one-thousandth of a horse-power ? Answer. — About 20.
Example 99.— If a battery having an E. M. F. equal
to E volts be used to charge a condenser of F farads, how
many foot lbs. of work are wasted in the charging?'
324 PRACTICAL ELECTRICITY. [Chap. VII.
Let K be the charge in coulombs held by the con-
denser when the P. D. between its coatings is E, then
K = EE,
and the store of energy equals, from § 176, page 323,
foot lbs.
2-712
The work done in t minutes by a battery of E. M. F.
equal to E volts, when a current of A amperes flows
through it, equals, from § 115, page 203,
44-25 A E< foot lbs.,
, •. the work done in t seconds is
——AEi foot lbs.
60
Now A t equals the number of coulombs that flow
through the battery in the time t, whether t be short or
long, and although when charging the condenser the
current will at first be very strong, and then will
gradually diminish until it becomes nought, we may
consider it to remain constant during a small fraction of
a second. Hence, if k be the number of coulombs that
pass during a time so short that the current may be
regarded as remaining constant during this time, the
work done by the battery during this time equals
^i:^ kE foot lbs.,
• 60
and this is true for each short time during the charging
Hence, the total work done by the battery equals
44-25
KE foot lbs.,
or ii^ FE2footlba.
60
£2
60
Chap. VIL] EXAMPLES. 325
Hence, the waste of energy during the charging equals
l^-^ ^]f Effect lbs.,
\ 60 2-712/
or J ^i^ F E2 foot lbs.,
or half the energy expended by the battery is wasted,
no matter what be its resistance, or the resistance of the
rest of the circuit.
Example 100. — If, instead of employing a battery
having an E. M. F. of E volts to charge the condenser,
E
we first charge it with a battery of — volts ; then increase
n
2E
the E. M. F. of the battery to and further charge
the condenser ; next increase the E. M. F. of the battery
to , and still further charge the condenser, and so
on, what will be the total waste of energy ?
The number of coulombs put into tiLe condenser in
the first charge equals
FE
and the work done by the first battery equals
44-25 F E2 , „
60 w2
The number of coulombs put into the condenser in the
second charge equals
JFE
and the work done by the battery equals,
44-25 FE 2E , „
X X foot lbs.,
60
n
826 PRACTICAL ELECTRICITY. [Chap. VIL
44-25 W
or ^^ 2 F — „ foot lbs., &c.
So that the total work done in charging the condenser
equals
44
60
'25 FE2 /
0 ^ 7*2 (
1 + 2 + 3+ . . . . +n\
44-25 FE2,T , .n
X (1 + ^) -
60 9^2 ^ ^2
44-25
60
(2^ + 1)
FE2 — +- foot lbs.
The store of energy in the condenser equals, as before,
FE2
2-712
foot lbs.,
quite independently of the way in which the condenser
has been charged. Hence, the waste equals
^FE2^ foot lbs.,
60 2 w
which becomes the same as before if n is unity, but on
the other hand becomes as small as we please if n be
made larger and larger. In fact, the more nearly we
make the rate of increase of the E. M. F. in charging
equal to the rate of the decrease of the P. D. between
the coatings of the condenser in discharging, the less
will be the waste in charging.
Example 101. —If an air condenser be formed of two
parallel metallic plates, each two square feet in area,
placed gVth of an inch apart, and charged with a P. D.
of 250 volts, what amount of work must be done in
separating the plates, so that the distance between them
is increased to Toth of an inch, if the wires used in
charging the condenser be removed before the plates are
Cbap. VII.] MEASURING CAPACITY ABSOLUTELY. 327
separated, so that the charge in the condenser remains
unaltered during the separation 'i
The capacity before separation equals from § 166,
page 307,
— — farads,
4-452 X 1012 X ife
or 1-940 X 10-9 ^
and after separation,
288
4-452 X 1012 X ^
or 6-467 x lO'io
therefore if K be the charge in coulombs in the con-
denser, and V the P. D. after separation in volts,
. K= 1-940 X 10-9 X 250
= 6-467 X 10-10 X V,
.-. V = 750 volts.
The store of energy, in the condenser before separation
equals
1-940 X 10-9 X 2503 ^ „
— ——— foot lbs.,
2-712 '
or 4-471 X 10-5 „
and the store of energy after separation equals
6-467 X 10-10 X 7502 ^ ^ ^,
-——- foot lbs.,
2-712 '
or 1-341 X 10-4 ^^
hence the work done in the separation equals
8-939 X 10-5 foot lbs.
177. Absolute Measurement of a Capacity. — The
absolute capacity of a condenser can be determined in
328 PEACTICAL ELECTRICITY. [Chap. VU.
farads by using a battery, whose E. M. F. we know in
volts, to charge it, when there is in the circuit a
galvanometer which has been calibrated so that the
number of coulombs or fraction of a coulomb that causes
any particular instantaneous swing is known. But this
absolute measurement of a capacity can more easily be
effected as follows, the only thing that is required to be
previously known being the value of a resistance in
ohms.
Let B (right hand, Fig. 125) be a battery of un-
known E. M. F. and resistance, but of such a large
Fig. 125.
number of cells, that when it is used to charge the
condenser c, F farads in capacity, a suitable instan-
taneous deflection is obtained on a reflecting galvano-
meter G. In order that we may use two P. Ds., whose
i-atio is known, shunt the battery with a large resist-
ance r, then if a portion r' (right hand. Fig. 125) of
this resistance bears to the whole r, a ratio equal to R,
it follows, without our knowing either r or r in ohms,
that V, the P. D. between l and n, the terminals of r',
bears to V, the P. D. between l and m, the terminals of ?',
the same ratio R.
Charge the condenser with the battery thus shunted,
by depressing the key k (left hand, Fig. 125), and let
the instantaneous deflection be dy. Next using V
Chap. VXL] MEASURING CAPACITY ABSOLUTELY. 329
(right hand, Fig. 125), send a steady current through
the galvanometer in series with a large resistance coil,
and let the value of the resistance of these two be o
ohms. Let d^ be the steady deflection so obtained, then
T. P I^ ^1
F= — X — X— ^
2 7r o ttg
For if K be the unknown number of coulombs re-
quired to charge the condenser to the unknown P. D. of
V volts,
K = F X V,
also from § 155, page 292, we know that
^ F A d.
K = - X -- X -1,
where a is the steady deflection that is produced by A
amperes. But since the deflection is proportional to the
current, and since the deflection d^ is produced by a
cur^nt of ^'amperes.
o
d,'
_ A X
R X
0
0
K
_ P
9r
R X
2 X
V.
— X
0
%
F
P R
27r 0
If the vibrations of the needle be damped, then the
above must be multiplied by 1 H , where I is the
Napierian logarithmic decrement (see § 157, page 296), in
order to obtain the correct value of F.
330 PRACTICAL ELECTRICITY. [Chap. VII.
This method was employed by the late Professor
Fleeming Jenkin, in 1867, in making the first absolute
measurements of the capacity of a condenser.
178. Statical Method of Comparing Capacities. —
Let r and f' be the capacities of the two condensers that are to be
compared. Bymeans of the arrangement shown to the left (Fig. 126),
charge the two condensers with the P. Ds. between the points l and
c, and c and m respectively. Let these P. Ds. be called V and V
volts, the numerical value of which it is not necessary to know.
Now, without discharging the condensers, separate the coating a
of the one and the coating b' of the other from the resistance coil,
and join these coatings together as shown to the right (Fig. 126), the
other coatings b and a' being j oined together as before. Let Vj be the
resultant P. D. in volts between a b' and b a', the numerical value
of which also need not be known, let K and- K' be respectively the
numbers of coulombs on the plates a and b' before discharge, then
K= FV
and K'r=-F'V',
also we know that K— K' is the charge in the compound plate
A b' of the joint condenser to the right (Fig. 126), of capacity F -|- F,
.-. K-K' = (F + FOVi.
Substituting, we have F V - F' V = (F + F') Vj,
.-. F _ V^+ Vi
F' ~ V - Vi*
In order to compare V, V, and Vi, observe the deflection pro-
duced by Vi on a suitable electrometer, and, without altering the
arrangement of the battery and resistance coil shown to the right
(Fig. 126), let two points, separated by a resistance rj be found, by
trial, such that the P. D. between them produces the same deflection
on the electrometer, then
V:V':Vi :: r:/:ri.
Consequently, F / + ^^i
F' "~ r - r/
If / and r be so selected by shifting the connection c (Fig.
126), in one direction or other, that K equals K', or Vj is nought,
then T? ^
This method of discharging one condenser into another, and
measuring the resultant P. D., may be employed not only when the
condensers are small, but when one or both of them are long
Chap. VII.] COMPARING CAPACITIES STATICALLY. 331
lengths of submarine cable, in which case, owing to the " retarda-
tion,^^ or time taken in charging or discharging the cable, the sim-
ple galvanometer method would give erroneous results unless the
period of the needle were made most inconveniently long so as to
insure the charge or discharge being completed before the needle
began to move.
If, however, the method just described of discharging one
condenser into the other, and measuring the resultant effect be
employed, not on account of the smallness of the capacities of the
condensers under comparison, but because one or both of them have
considerable retardation, then a galvanometer can be used to measure
approximately the resultant P. D., the test giving perfectly accurate
results when the point c is so selected, by trial, that the discharge
of the compound condenser through the galvanometer is nought.
Fig. 126.
If the resultant charge be not absolutely nought, we can, in-
stead of making a great number of tests to find the point c, for
which it would be absolutely nought, and which may occupy more
time than is at our disposal, correct approximately for a small re-
sultant discharge as foUows : —
Let d be the resultant deflection, and let d' be the deflection
obtained on charging the compound condenser with the P. D. be-
tween two points in the resistance coil, separated by a small re-
sistance ^2 ; then, if, as before, r-i be the resistance between two
points in the coil having a P. D. between them equal to Vj, but
which we cannot now find directly, as we are not using an electro-
meter, it follows, disregarding the retardation, that
d r J
I >^'A.^r
Hence, t_ — ____!_,
F- d *
332 PRACTICAL ELECTRICITY. [Chap. VIL
F d'r-dri
179. Measuring Specific Inductive Capacity. — If
we know the area A of each of the coatings of a con-
denser in square centimetres, and t the thickness of the
dielectric in centimetres, then, from § 169, page 311, it
follows that i, its specific inductive capacity,
__ F X 1-131 X 10^3 X t
"" A '
where F is the capacity of the condenser in farads, which,
if large enough, can be measured either absolutely by
the method described in § 177, page 328, or relatively
by comparison with another condenser, whose capacity is
known in farads, using the method described in § 174,
page 319.
Frequently, however, we desire to measure the specific
inductive capacity of a comparatively small specimen of
an insulating material, too small to be employed in
making a condenser of large capacity, unless the dielectric
were made so thin that it would be extremely difficult to
determine its thickness accurately. In such a case we
may employ the statical method described in § 178,
page 330, of comparing the capacity of a condenser
made with the specimen of insulating material with the
capacity of a condenser of somewhat similar dimensions,
but having air for the dielectric. To use this method,
however, we must have an electrometer of considerable
sensibility, with its quarter cylinders far better insulated
from one another and from the outside of the instrument
than are those in the instrument illustrated in Figs. 47
and 48, § 75, page 131. We also must have a charge
and discharge key of high insulation, and enclosed in a
metallic box, so as to be shielded from induction (see
§ 51, page 99). This statical method, therefore, of
comparing the capacities of two condensers, each of small
capacity, although susceptible of giving extremely accurate
Chap. VII.] MEASURING SPECIFIC INDUCTIVE CAPACITY. 333
results when carried out with the various precautions
that would be adopted by a skilled experimenter, is alto-
gether unsuitable to be employed by a beginner.
The following method, however, based on a plan of
experimenting originally suggested by Dr. Sauty, has
been used by the author with good results. c and c'
(Fig. 127) are the two condensers of small capacity, M
and M', that we desire to compare ; a and h are two ad-
justable resistances wound double in the ordinary manner
employed in constructing resistance coils (see Fig. 7, § 12,
Fif?. Y>1.
page 28), K is a key, turning about its centre and making
contact either at \ or at k^^ so that by moving the
handle down and up the two condensers can be charged
by the battery b or discharged, and t is an ordinary
Bell telephone connecting the points p and q, and
which is an extremely delicate instrument for detecting
small rapid fluctuations in the strength of a current passing
through it. If the key K be alternately moved up and
down there will be a succession of currents in opposite
directions through the telephone, unless the potentials at
p and Q always remain equal to one another, and in
order that the P. D. between these two points may be
334 PRACTICAL ELECTRICITY. [Chap. VII.
always nought, the rise or fall of potential at each of
these points must be the same in the same time. This
condition will be fulfilled when the quantities of elec-
tricity that flow into, or out of, the two condensers in
the same time, are directly proportional to their capaci-
ties, and when there is no sensible retardation. Further,
if the potentials at p and q are equal to one another, the
quantities of electricity that flow through the two wires,
o p and o Q respectively, must be inversely proportional
to their resistances a and h. Hence, combining these
two conditions, no sound will be heard in the telephone
if a and h are adjusted until
M _^
W~~ a
The substance of which we desire to measure the
specific inductive capacity, as, for example, a sheet of
glass or a sheet of guttapercha,
should have pasted on each side of
it sheets of tinfoil of equal size,
and about one inch smaller all
round than the sheet of dielectric,
so as to secure little surface leakage.
If the sheet of dielectric be itself
Fig 128 small, the space left uncovered with
tinfoil must be less than one inch in
width, but in that case the uncovered portion should be
carefully cleaned and dried. It is also desirable for the
purpose of diminishing this surface leakage to rest the
condenser on a block b, as shown in Fig. 128, so as to
keep the underneath portion of the sheet of dielectric D
that is not covered with a sheet of tinfoil, corresponding
with T above, from touching anything.
180. Standard Air Condenser. — The standard air
condenser may be conveniently constructed, as shown
in Fig. 129, of thin slabs of plate glass about one-eighth
of an inch thick, coated on both sides with tinfoil.
These sheets of glass do not act as the dielectric, but
Chap. VII.]
STANDARD AIR CONDENSER.
336
merely form convenient supports, with very plane sur-
faces, for the sheets of tinfoil, hence the two sheets of
tinfoil on the two sides of any one of the slabs of glass
must be electrically connected. With every alternate
slab 1, 3, 5, &c., the sheets of tinfoil are pasted over the
Fig. 129.
whole surface of the glass, and may be each about one
square foot in area, while in the case of the other set
2, 4, 6, &c., there is one inch left all round the glass not
coated with tinfoil, as seen on the top" plate p p of the
condenser in the figure. This is in reality the top plate
but one, the top plate T t, which is wholly covered with
tinfoil, having been removed to enable the plate P P to be
seen. The first set form together the outer coating, and
336 PRACTICAL ELECTRICITY. [Chap. VIL
their terminal A is connected with s (Fig. 127), while all
the smaller sheets of foil form the inner coating, and
their terminal b, mounted on a block of ebonite, is con-
nected with p. The glass slabs are piled one on the
top of the other, but separated by fragments of glass
pp, all of the same thickness, conveniently about one-
tenth of an inch ; and there is one more of the
slabs with the larger sheets of tinfoil on it than of the
others, so that there is one of the former both at the
bottom and at the top of the condenser when it is thus
built up. The glass plates are prevented from sliding
over one another when the condenser is moved, by their
corners fitting into grooves in the four ebonite pillars
E, £, E.
The capacity of the standard condenser, in farads,
oquals
^A
4452 X 1012 X i
where A is the sum of the areas, reckoned in inches, of all
the smaller sheets of tinfoil, and t is the thickness of
one of the little glass fragments.
The capacity of the experimental condenser equals
4-452 X 1012 X <'^
where A' is the area of one of the tinfoil coatings, t' the
thickness of the sheet of dielectric under test, and i its
specific inductive capacity. Hence, if the resistances a
and h (Fig. 127) are so adjusted that no sound is heard
in the telephone,
a A «'
1= - X - X -.
h A' t
The construction of the Bell's telephone, such as may
be used in the previous experiment, is shown in Figs. 130
and 131, where m is a permanent magnet, terminated at
the right-hand end (Fig. 130) by a piece of soft iron of
Chap. VII.]
THE BELL TELEPHONE.
337
the same thickness. Round this piece of iron is a coil of
wire h b, the ends of which d d are led to the terminals
V V. Close to the end of the piece of soft iron, but
not touching it, is a thin plate of ferrotype iron c e. The
Fig. 130.
piece of soft iron is magnetised by the permanent magnet
7)1, and thus attracts the centre of the thin plate of iron,
and the amount of this attraction is varied by any cur-
rent that passes round the coil h. Hence, if there be
rapid fluctuations in the strength of the current passing
round this coil, and still more, if there be rapid altema-
Fig. 131.
tions in the direction of the current passing round this
coil, the thin iron plate will be set in rapid vibration,
and a sound will be emitted. If the telephone be well
made, and if the ear be placed near the opening shown
at the right hand in Fig. 130, and at the left hand in
Fig. 131, the sound produced by even extremely small
w
538
PRACTICAL ELECTRICITY.
[Chap. Vll.
alterations in the current strength, can be heard, if they
follow one another with sufficient rapidity.
181. Every Charged Body forms One Coating of a
Condenser. — In practice, as already explained, a con-
denser is the name given to two sets of sheets of metal
so arranged that the one set has a large capacity rela-
tively to the other ; but, in reality, every charged body
forms a condenser with some other body ; it may be with
the walls of the room, or the ceiling, or the table, or the
body of the experimenter, or with all of them ) hence
we see that the statement made at the foot of page 109,
that when one conducting body A is entirely surrounded
by another conducting body b, the quantity of electricity
on A is directly proportional to the P. D. between a and
B as long as the position of A, relatively to b, is abso-
lutely fixed, is only another way of saying that the
capacity of A relatively to b is constant as long as their
relative positions are unchanged.
In § 67, page 120, it was explained that the poten-
tial of the charged metal plate P could be diminished by
bringing near it the
metal plate m, connected
with the earth. We
now understand that
this arises from the
capacity of p relatively
to M being increased by
approaching them, in
consequence of which
the potential of P, cor-
responding with a given
charge on it, is dimin-
ished (see § 167, page
308).
182. Capacity of a
Spherical Condenser. — If a metallic sphere a (Fig. 132)
of a centimetres' radius be insulated concentrically inside
another hollow metallic sphere b of 6 centimetres' radius,
Fig. 132.
Chap. Vn.] CAPACITY OF A SPHERICAL CONDENSER. 339
and if the dielectric separating them be air, the capacity
of A, relatively to b, can be proved to be
farads.
9 X 10^^ ih-a)
This last expression can be written in the form
9x 10
"0-"^
from which we see that as h grows greater and greater,
the capacity of A grows smaller and smaller. Con-
sequently, although we have no experience of a single
charged body insulated alone in space, we can see what
is the limit to which the capacity of A approaches, as h
becomes larger and larger. The value of this limit is
obtained by making b equal to infinity, when the capacity
of A becomes
— — farads,
9 X 10" '
and this is practically the capacity of a sphere when, as
in the case of A, Fig. 43, page 121, it is so far away from
other bodies as to be practically beyond the range of
their inductive action.
But because we can calculate the capacity of a body
when it is so far away from other bodies as to be practi-
cally beyond the range of their inductive action, it must
not be imagined that we can have a charged body exist-
ing alone in space. Indeed, as seen in § 60, page 115,
we cannot produce only a single quantity of electricity,
since equal and opposite quantities are produced simul-
taneously, therefore it is impossible to have one body
charged positively or negatively without some other
body existing with an equal and opposite charge on it.
And just as we have no experience of a single
340
PRACTICAL ELECTRICITY.
[Chap. VII.
charged body existing by itself, so it is equally impossible
to obtain two bodies charged with the same kind of
electricity without a third one oppositely charged. Al-
though, therefore, we are accustomed to speak of two
positively or of two negatively electrified bodies repelling
one another as if this action could take place without the
presence of any third body, we must not allow this very
convenient form of ex-
pression to cause us to
forget that all our ex-
perience of the action
of electrified bodies is
derived from experi-
ments made inside a
room, the walls, ceiling,
and floor of which are
more or less good con-
ductors, and which
form condensers with
the electrified bodies in-
side the room. For ex-
ample, if A and c (Fig.
133) be two spheres
electrified positively,
and placed inside a
conducting room b b,
the distribution of the
density will be roughly as in the figure, the density being
greatest where the plus or minus signs are nearest to-
gether. If A and c be free to move, then, as is well
known, they will separate from one another, and ap-
proach the sides of the room. This action is usually
regarded as being caused, partly by the repulsion of the
positive electricities on A and c, and partly by the at-
traction of the positive electricity on each of the bodies
by the negative electricity on the side of the wall ad-
jacent to the two bodies respectively. But as we have no
experimental evidence of what would happen if A and c
Fig. 133.
Chap. VII.] CONDENSER METHOD OF COMPARING E. M. Fs. 341
could exist with their positive charges apart from B b, it
may be that it is the attraction of the opposite elec-
tricities that causes a and c to separate, and that there
is no repulsion at all between the similarly electrified
bodies a and c ; and this, of course, is true whether A and
c be spheres inside a conducting room with flat walls,
ceiling, and floor, or
whether they be conduc-
tors of any shape inside
another of any other
shape, as shown in Fig.
134.
Example 102.— What
is the capacity of the
earth regarded as a sphere
insulated in space *? ^^^- ^^•
Answer. — The mean
radius of the earth is 6-3703x10^ centimetres, hence its
capacity is 0*0007078 farads, or roughly 708 microfarads,
which is the capacity of about 2,000 miles of ordinary
submarine telegraph cable.
183. Condenser Method of Comparing the E. M. Fs.
of Current Generators. — We have already seen (§ 132,
page 234) that with cells which polarise, as it is called,
the ordinary galvanometer methods of comparing KM.Fs.
cannot be employed to obtain accurate results, and that
a null method like that of PoggendorflTs is much to be
preferred. When, however, a condenser and a suitable
reflecting galvanometer for measuring capacity are at
hand, the following method may be employed instead of
Poggendorff^'s. Charge the condensers successively with
the two current generators, and in each case measure the
charge or discharge with the galvanometer, then, since
the deflections are proportional to the charges or dis-
charges (§ 160, page 299), and since these charges are
proportional to the E. M. Fs. employed, it follows that
the E. M. Fs. are proportional to the deflections.
If the plates of the cell have only a very small surface
342 PRACTICAL ELECTRICITY. [Chap. VII.
in contact with the liquid, the polarisation arising from
the flow of electricity into the condenser to charge it
may be sensible if the condenser have a large capacity.
Hence, in such a case, it is important to use a condenser
of as small a capacity as can be employed to give a
satisfactory deflection with the most delicate galvano-
meter available. Such a precaution is especially neces-
sary when experiments on the E. M. Fs. of cells made
of simple pieces of wire dipping into various liquids are
performed.
184. Condenser Method of Measuring the Resistance
of a Current Generator. — We have seen, § 115, page 204,
that if a current generator having a fixed E. M. F. equal
to E volts, and a resistance of h ohms, be shunted with a
resistance of r ohms, the P. D. at the terminals will be
X E volts.
T + h
If, then, we employ first the generator unshunted to
charge the condenser, and obtain, on charging or on dis-
charging through a suitable galvanometer, a first swing c?i
of the spot of light ; second, if the generator be shunted
with a resistance r ohms, and we obtain, on charging or
on discharging, a first swing dc^, we know that
^ = E ^ ^ E,
d^ r -\- h
With cells that polarise it is very important that the
battery should be shunted with the resistance r only at the
moment of charging the condenseVj and that the act of
disconnecting the battery from the condenser should also
disconnect the shunt. This may be conveniently effected,
without the employment of any special key, by joining
up the arrangement as shown in Fig. 135, the key in the
Chap. VII.] CONDENSER TEST OF A BATTERY RESISTANCE. 343
figure being exactly the same in principle as that shown
in Fig. 121, page 320, but not possessing such high
insulation, as this is unnecessary with the present experi-
ment. One pole Q of the battery b is permanently con-
nected with one end of the resistance r, with one coating
Cj of the condenser, and with the upper screw Sg of the
key ; the other pole p of the battery is insulated as long
as the contact at Si is broken. On depressing the lever
the contact at Sg is broken and that at s^ made ; this has
the effect of connecting the pole p of the battery to the
Fig. 135.
other end of the resistance r and to the other coating Cg
of the condenser through the galvanometer g, hence the
condenser is charged through the galvanometer with the
cell shunted. On liberating the key, whicli should be
done directly the first swing is completed^ the contact at
Sj is broken and that at So made ; p is therefore discon-
nected from the shunt and the galvanometer, and the
condenser is discharged through the galvanometer.
To observe the charge with the battery unshunted, the
infinity plug in r must be withdrawn, or one of the ends
of the resistance r must be disconnected from the rest of
the circuit.
344 PRACTICAL ELECTRICITY. [Chap. VII,
185. Measuring a Resistance by the Rate of Iioss
of Charge. — When a resistance of not merely thousands of
megohms, but of millions of megohms has to be measured, the
galvanometer method described in § 151, page 278, is not sensitive
enough, unless an enormously large battery be employed, and a
mode of testing depending not on measuring the rate of leakage
but on measuring the amount that has leaked in a given time has
to be resorted to, as follows: — If a charged condenser have
its two coatings connected by a resistance, it will be discharged
with more or less rapidity depending on the magnitude of the
resistance, and the capacity of the condenser. If F farads be the
capacity, r ohms the resistance, and if the P. D. between the coat-
ings be V volts at a certain time, and V volts t seconds afterwards,
then we can prove that
0-4343 t
*■= V"'
hence the resistance r may be ascertained if we know F, V, V,
and t.
To prove this formula we shall assume that the whole interval
t seconds, during which the discharge is observed, is subdivided into
a great number n of very small equal intervals of time t, so small
that during the whole of any one of these small intervals, the P. D.
between the coatings may be supposed to remain constant, so that
instead of the P. D. falling gradually from V volts to V volts, we
suppose it to fall by n small jumps, one jump being made at the
end of each interval. The same sort of approximation to the
truth is made when a curve is supposed to be formed of a very
great number of very short straight lines, each two adjoining
straight lines differing very slightly from one another in direction,
since, instead of the gradual change of direction which occurs in
going along a real curve, we have a discontinuous change in
moving along the succession of short straight lines.
At the commencement, the number of coulombs in one coating
of the condenser is
FV,
and during the first interval the quantity in coulombs that flows
out of the one coating into the other is
V
BO that the quantity that will remain in this coating is
FV-IrorFvA -—\\
r \ Yrf
Chap. VII.] MEASURING RESISTANCE BY LOSS OF CHARGE. 345
hence, the P. D. hetween the coatings at the end of the first
interval equals
0-F>
During the second interval of t seconds the number of
coulombs that will flow from one coating into the other equals
r\Yrf
80 that the quantity that will remain in each coating will be
or (fV-It)(i-^),
or Fy( 1 _ —I coulombs.
V F r/
Similarly, the number of coulombs remaining on each coating at
the end of the third interval equals
V Fr^
and at the end of the n, the interval that is at the time ^
tut this is equal to F V,
.-. Fv/i_ JL.Y = ¥Y\
or dividing both sides by F, and substituting — for t, it follows
that
346 PRACTICAL ELECTRICITY. [Chap. VH.
and this is more and more true the larger n be made. But it can
be shown mathematically that when n is infinitely great
t
(-
Frnf
¥r
when 1
6 stands for 2 -7 1828
. So that
t
''""Flog..
Consequently, converting the logarithm to the base e to a
logarithm to the base 10, by the method given in § 158, page 296,
we have
0-4343 1
If an electrometer, with well-insulated quarter cylinders, be
available, then the loss of potential can be easily observed by
attaching the two coatings of the condenser to the opposite pairs
of quarter cylinders, giving the condenser a charge, and observing
the times at which the spot of light passes two definite positions on
the scale, for V and V may be measured in any units, since we
have merely to deal with the ratio of V to V. In this way the
insulation of even a short length of weU-insulated cable can be
measured. For, as the cable is shorter, and r is larger, F is pro-
portionately smaller, so that the time the P. D. takes to fall from
one given value to another is independent of the length of the
cable.
186. Rate of Loss of Charge from Leakage through
the Mass depends on the Nature of the Dielectric
only, and not on the Shape or Size of the Condenser.
— Not merely is the time the P. D. takes to fall from one given
value to another independent of the area of the coatings of the
condenser, but it is independent of the thickness of the dielectric.
Take the case of a condenser with flat parallel plates. Then, if A
be the area of one of the coatings in square inches, d the distance
Chap. VII.] RATE OF LOSS DEPENDS ON DIELECTRIC ONLY. 347
between them in inches, and s the " specific resistance,''^ or resistance
per cubic inch of the dielectric.
d X »
and from § 169, page 311, if i be the specific inductive capacity of
the dielectric,
F = ix ;
4-452 X 10^2 X d
, • . if < be the time in seconds during which the P. D. falls
from V to Y\
dx s _ 0-4343 < X 4-452 x 10^^ d
» A log-io —
, V
the right-hand expression depending only on the specific re-
sistance, and specific inductive capacity of the dielectric, and not
on its shape or siize.
So in the same way with a cylindrical condenser the capacity
in farads, as we have seen from § 168, page 308, and § 169, page
31i, is
. ^ 2-413 I
1013 log.joD-log.io^
where t is the specific inductive capacity of the dielectric, I the
length of the condenser in centimetres, and D and d the diameters
of the coatings. It may also be shown that if s' be the resistance,
in ohms, per cubic centimetre of the dielectric, r, the resistance of
length I of the cylindrical condenser is
(log.joD-log.io^O-
0-8686 TT?
Consequently,
log-io Y' 4-912 X 1013
348 PRACTICAL ELECTRICITY. [Chap. VIL
It has to be remembered that whereas for the condenser with
flat parallel plates, s was the resistance per cubic inch of the dielec-
tric, here s' is the resistance per cubic centimetre. Hence, since the
resistance is proportional to the thickness, and inversely as the
sectional area,
_ 2-54 ^
2-542 '
or «' = 2-54 a ;
that is, the resistance per cubic centimetre of any substance is 2 "54
times the resistance per cubic inch. The specific inductive capacity,
r, is iridependent of the unit of length or area. Hence, substi-
tuting the value for «', we obtain
Y
^^' *•* V' 1-934 X 1012
which is the same expression as that obtained with flat parallel
187. Galvanometric Method of Measuring Resist-
ance by Loss of Charge. — In the formula given in § 185,
page 344, we may substitute for V and V the number of cou-
lombs K and K', on one of the coatings of the condenser when the
P. D. between the coatings is V and V' volts, so that
0-4343 t
r = —
^l«g-io|
If the capacity of the condenser be sufficiently large, K and
K' can be measured by charging the condenser through a gal-
vanometer at a certain moment, and discharging it again at the
end of t seconds, using the arrangement shown in Fig. 123, page
322. To enable the lever L of the key, seen more plainly in Fig.
121, page 320, to be left without completing the contact at Sj
or at S2 during the time the condenser is left insulated, the screw
which makes the upper contact 83 should be screwed out so far
that it would require a slight upward pressure to be given to the
lever to cause it to make this upper contact. If the resistance to
leakage be very large, K and K' will be nearly equal to one
another imless t be taken inconveniently long. This difficulty
may be overcome by using a large battery, and charging the con-
denser with the galvanometer shunted at the beginning of the
Chap. Vn.J POWER OF SHUNT WITH DISCHARGE. 349
time t, and then charging it again with the galvanometer un-
shunted, and therefore in a much more sensitive condition at the
end of the time t. In this way K and K - K' will be measured, and
by properly choosing the shunt, the second test may be made as
delicate as the first. Since, however, as mentioned in § 174, page
319, a difficulty is introduced when comparing two quantities of
electricity if the galvanometer be shunted in one case and not in
the other, this method is not a perfectly accurate one unless the
following correction be introduced.
188. Multiplying Power of a Shunt used in Mea-
suring a Discharge. — When a quantity of electricity is
passed through a shunted galvanometer, the quantities that pass
respectively through the galvanometer and shunt are inversely as
their resistances exactly as in the case of a steady current ; but
when, after the discharge has been completed, the needle begins
to move, its motion induces a current in the galvanometer and
shunt in such a direction as to tend to stop its motion. This in-
duced current, therefore, damps the motion of the needle, and we
have, therefore, to use the formula for damped vibrations given in
§ 157, page 296. It can, however, be proved mathematically that
with a given galvanometer, and with a given adjustment of the con-
trolling magnet, ^c, the damping in this case has simply the effect of
increasing the resistance of the galvanometer by a definite amount, in-
dependently of the resistance of the shunt. So that if g be the actual
galvanometer resistance, and s that of the particular shunt em-
ployed, the multiplying power for a discharge is
s-\-g-\-g'
where ^ has a definite value, independent of that of s, for a given
galvanometer with a given adjustment of the controlling magnet,
&c. Instead, therefore, of employing the formula for damped
vibrations, to do which we must measure the decrement when its
vibrations are damped, we may simply determine the constant g' in
the following way : —
Charge a condenser with a small P. D., say of Vj volts,
through the galvanometer unshunted, obtaining a first swing d^,
say. Next, having discharged the condenser, shunt the galvano-
meter with any convenient shunt of resistance s, increase the P. D.
to a suitably larger value Vg volts, and charge the condenser
through the shunted galvanometer, obtaining a first swing d^.
Then, since the quantities which pass into the condenser are pro-
portional to Vi and Vg,
X? _ *_±iL±/ x^
V, 8 <f,*
350 PRACTICAL ELECTRICITY. [Chap.VIL
or the multiplying power of the shunt,
and g+g'zzsCh.Y^-A
As Vj and Vg only occur in a ratio, we do not require to
know their absolute values in volts, and the simplest method of
obtaining two P. Ds. having a known ratio is that given in § 150,
page 278.
Example 103. — On charging a slightly leaky condenser
through a galvanometer of 1,000 ohms' resistance, shunted with the
yipth shunt, a deflection of 230 scale divisions is obtained. The
condenser is then insulated, and at the end of half a minute it is
again charged but with the galvanometer unshunted, and a deflec-
tion of 112 scale divisions is obtained. What is the resistance of
the condenser ?
To ascertain the value of the first deflection in farads, as well
as to find the increased multiplying power of the shunt for a dis-
charge, let us charge a well-insulated condenser of known capacity,
say ^rd of a microfarad, with ^the same P. D. as was used in the
previous experiment ; let this give a deflection of 175 scale divi-
sions with the galvanometer unshunted. Next discharge the con-
denser, shunt the galvanometer with, say, the same shunt as
was used before, increase the P. D. employed, and again charge
the condenser, obtaining, say, a deflection of 295 scale divisions.
Let these two P. Ds. be those between the points S and T, Fig. 101,
page 278, and L and M, and let the ratio of the resistances of q
and j9 be in the ratio of 10 to 1,736.
The multiplying power of the shunt for a discharge equals
s-\-ff-\-9' _ 1736 ^^ m^
« 10 295*
= 103,
therefore the capacity of our slightly leaky condenser is
103 ^x — farads,
175 3 X 10«
or 45-12 microfarads.
Next, K being the number of coulombs in one coating of om
Chap. Vn.] PRODUCTION OF LARGE P. Ds. 361
slightly leaky condenser at the moment of charging, and K the
quantity at the end of half a minute,
-^r- = 112 -T- 230 X 103,
Hence,
. log. 10 I, =0-0021.
0-4343 x_30_^j^^
t^ X 0-0021
10«
Answer. — 137-5 megohms.
Lai'.ge Potential Differences.
189. Production of Large Potential Differences. —
When any two dissimilar substances are brought into
contact, there is a certain P. D. set up between them in
consequence of what is known as the " contact potential
difference." The two substances, therefore, become
charged, like the two coatings of a condenser, with
equal and opposite amounts of electricity, depending on
the contact P. D., the proximity of the two bodies and
their size. If either, or both, of these bodies be an in-
sulator, or be held by an insulating handle, some, or all,
of the charge will remain when the bodies are separated.
If the bodies be separated in such a way that practically
all the points of contact are broken at the same time,
then all the charge will remain on each of the bodies if
they be properly insulated. As the distance between
the bodies increases the capacity of the condenser rapidly
diminishes, hence the P. D. between the bodies rapidly
increases. In this way a P. T>. of many hundreds, or
thousands, of volts can easily be produced by bringing a
piece of dry, clean glass into close contact with a piece
of silk, or a piece of dry, clean ebonite into close contact
with a piece of cat's-skin, and then separating them ; and
352 PRACTICAL ELECTRICITY. [Chap. VIL
just as work has to be done in separating the two plates
of a charged condenser {see Example 100, page 326), work
has to be done in separating the glass from the silk, or
the ebonite from the cat's-skin, and the power that the
glass or ebonite has to give a spark when the knuckle is
brought near it, arises from the condenser possessing a
store of potential energy. {See § 176, page 322.) The
ebonite forms one of the coatings of this condenser, and
the surface of the room the other, because, as the cat's-
skin is not a good insulator, the charge of positive elec-
tricity induced on it when it is in contact with the
ebonite, spreads itself over the walls, ceiling, and floor of
the room on the separation. As explained in § 61, page
115, the object of rubbing the glass with the silk is to
bring all parts of the surface of the insulating glass into
successive contact with the silk.
The well-known cylindrical and plate-glass frictional
electrical machines are merely contrivances for bringing
different portions of the surface of a cylinder, or a sheet
of glass, successively into close contact with a silk rubber,
and separating them again. The electrical energy pro-
duced by such an apparatus depends simply on the work
required to perform the separation of the positively elec-
trified portions of glass from the negatively electrified
rubber, whereas the actual power expended in turning
such a machine is mainly wasted in overcoming friction
and producing heat. Hence, such frictional machines are
extremely inefficient converters of mechanical energy into
electrical energy, and they are, therefore, rapidly becoming
obsolete, and being replaced by the much more efficient
influence Tnachines. {See § 194, page 361.)
190. Condensing Electroscope. — The increase of
P. D. between the two coatings of a charged condenser,
produced by separating the plates, may be employed to
cause an ordinary gold-leaf electroscope to indicate the
P. D. existing at the terminals of two or three cells in
series. For, let the plate m. Fig. 42, page 120, be con-
nected electrically with the tinfoil coating of the gold-
Chap. VII.J CONDENSING ELECTROSCOPE. 353
leaf electroscope, and placed close to the plate p ; then
let them be connected with the terminals of, say, three
Daniell's cells in series, which will cause them to be
charged with a P. D. of about 3*3 volts. Now, discon-
nect p from the cells, and remove M altogether, then the
P. D. in volts between the gold-leaves and the tinfoil
coating of the electroscope will become 3*3 multiplied by
the ratio of the capacity of p when m was close to it, to its
capacity when M has been removed far away, that is, when
p forms a condenser with the walls and ceiling of the
room, and with the tinfoil coating of the electroscope ;
since, with a given charge on the coatings of a condenser
the P. D. between the coatings is inversely as the
capacity {see § 167, page 308). This ratio will be the
greater the nearer M was brought to P during the charg-
ing, and may easily be made 100 or more (so that the
P. I), between the gold-leaves and the tinfoil coating is
now between 300 and 400 volts) by having the surfaces
of the plates carefully coated with a layer of shell-lac,
and by simply resting M on P. Strictly speaking, the
ratio of capacities to be considered is that of P plus that
of the gold-leaves when M is close to P, to that of P plus
that of the gold-leaves when m is far away ; and although
the capacity of the gold-leaves is insignificant in compari-
son with that of p when m is very near p, it is not so
when M has been removed. The above will be practi-
cally the same whether m be disconnected or not from
either the tinfoil coating or the cells, before it is re-
moved.
In order that the distances separating all parts of m
and p may be very small, their surfaces must be made
quite plane, and it is difficult to do this unless the plates
be fairly thick. But if they are thick they will be too
heavy to rest on the stem of the electroscope, hence it is
better to support p as the plate A (Fig. 29, page 88), is sup-
poi-ted, by means of an insulating stand having a fairly
strong glass rod, and to connect it with w of the electro-
scope by a thin piece of wire.
354 PRACTICAL ELECTRICITY. [Chap. VIL
191. Calibrating a Gold-Leaf Electroscope. — If the
ratio, r, say, that the sum of the capacities of p and of
the gold-leaves when m is placed in a fixed position near
p bears to the sum when M is far away, be accurately
known, then a gold-leaf electroscope, which will not in-
dicate directly a P. D. of less than 100 or 200 volts, may
be calibrated for any divergence of the leaves by the
employment of some ten or twelve cells. For if p and
M, when near together, be charged with one cell, and
then M be removed, and the divergence of the gold-leaves
dy noted, then P and m be charged with two cells, m be
removed, and the divergence c?2 noted, &c., these diver-
gences (ij, c?2, &c., will correspond with a P. D. between
the gold-leaves and the tinfoil coating of r E, 2 rE, &c.,
volts, where E is the E. M. F. of one cell, and which is
1-104 volts if the cells be Daniell's cells made with
equidense solutions of copper and zinc sulphate, and if
yure zinc and copper plates 'be employed {see §119,
page 211).
It would be practically impossible to determine this
ratio, r, by calculation, owing to the difficulty of calcu-
lating the capacity of p, and the gold-leaves when M was
removed. To determine it experimentally would be
nearly as difficult as calibrating the gold-leaf elec-
troscope directly by experiment. We must, therefore,
employ some condenser, the capacity of which can be
made to have two very distinct values, both of which are
large compared with the capacity of the gold-leaves,
having a known ratio to one another of about 100 ; or we
may employ the arrangement suggested by Sir William
Thomson, in 1885, for increasing a P. D. in a known
ratio, and which is shown symbolically in Fig. 136. A,
B, c, &c., are well-insulated condensers of not necessarily
equal capacities, joined up in series, the outer coating of
the first a being connected with the outside of the electro-
scope, and the inner coating % of the last with the gold-
leaves. A well-insulated battery, ss, of a convenient
number of cells, having an E. M. F. equal to E volts, has
Chap. VII.J CALIBRATING A GOLD-LEAF ELECTROSCOPE. 355
a I c d e z
r\ r\ r\ /\ rS r\ r\
its terminals connected, first with a and 6, then, instead,
with h and c, then with c and d, &c. On the battery ter-
minals being connected with a and b, the coatings of the
first condenser will have a P. D. of E volts produced
between them, and similarly on the battery terminals
being connected with b and c a P. D. of E volts will be
produced between b and c, therefore the P. D. between a
and c will be 2 E volts.
Again, on connecting the
battery terminals with c
and d, the P. D. between
a and d will become 3 E
volts, &c. Hence, if there
be 100 condensers in series,
and if the battery be moved
along so that its terminals
make successive contacts
with the pairs of coatings
of each of the condensers,
the P. D. between a and z,
that is between the outer
coating of the electroscope
and the gold - leaves, will
become 100 E, and by
making E first, say 2 volts,
next 3 volts, and so on,
the electroscope can be calibrated with P. Ds. of 200,
300, &c., volts.
In the last paragraph it is stated that the coatings of
the condensers are well insulated from one another, but
if the battery terminals s s be rapidly moved backwards
and forwards so as to make 7'apid successive contacts with
the coatings of the various condensers, it will only be
necessary for the insulation of the condensers to be fairly
good, as there will be no time for leakage to take place
between the successive contacts of the coatings of each
condenser with the battery terminals.
The following gives the result of the approximate
Fig. 136.
356
PRACTICAL ELECTRICITY.
[Chap. VII.
Angle
between the gold-
leaves.
26^
42°-6
60^-2
92"-7
calibration of a gold-leaf electroscope, the gold -leaves
being about 1^ inch long : —
P. D. between the leaves and
the tinfoil coating
in volts.
600
750
1,000
1,500
192. Electrophorus.— The oldest form of influence
machine is the " elect^-ophorics" which consists of a plate of
some insulating sub-
stance i (Fig. 137),
usually ebonite in the
modern electropho-
rus, fastened into a
metal backing b, and
a movable metal plate
p, into which screws
a metal ferrule at-
tached to an insu-
lating rod or handle
R. The electrophorus
can be made to give
a succession of either
positive or negative
charges of high po-
tential by the varia-
tion ofcaj)acity of the
condenser formed of
the ebonite and the
plate P, produced by
altering their distance
from one another
The ebonite, on being rubbed with a piece of cat's-
skin, becomes negatively charged, and forms a condenser
of fixed capacity with the uninsulated backing b, the upper
surface of which is therefore charged positively. Further,
this condenser-action causes the negative charge produced
Chap. VII.1 THE ELECTROPHORUS. 357
on the upper surface of the ebonite to be attracted a small
distance downwards into the insulating substance of the
ebonite, and so prevents the charge being easily removed
by the metal plate P when it is laid for a short time
on the ebonite. If this plate be held by the insulating
handle r, and placed on the ebonite, the potential of
the ebonite will be slightly diminished numerically — that
is, become less negative — {see § 67, page 120), and the
plate p will be raised to a fairly high negative potential,
the density on its lower surface being positive, and on
its upper negative {see § 69, 5, page 124) ; p, in fact,
forms a condenser with the ceiling and walls of the room.
If now, by means of the insulating handle, held at the
extreme end to diminish the surface leakage as much as
possible, p be removed again without being touched, its
negative potential will grow less and less as its distance
from the ebonite gi'ows greater and greater, and the
density on its upper and lower surfaces will also be
diminished, until at last when P is beyond the range of
the inductive action of the ebonite it will be simply an
uncharged body at a potential nought.
But if, on the other hand, while P is resting on the
ebonite, it be connected with the backing, b, or with the
earth, by means of a wire, or more simply by touching
it with one's finger, its potential will be reduced to
nought, and the potential of the ebonite will be numeri-
cally diminished. Hence, some of the positive charge
previously induced in the backing will flow away, all the
negative charge on the upper surface of p will also dis-
appear, and some more positive electricity will be
attracted to the lower side of p, the density on its upper
surface will become, therefore, nought, and on its lower
surface more positive than before. p and b together
now form the earth coating, and the ebonite the insu-
lated coating, of a condenser. On removing p by means
of the insulating handle R, its potential rapidly rises
positively, and that of the ebonite increases negatively.
When p has been removed some little distance from the
358 PRACTICAL ELECTRICITY. [Chap. VII.
ebonite, its potential becomes high enough to enable it
to give a positive spark"**" to a conductor brought near it.
And as the ebonite is not sensibly discharged by the
action of placing p on its surface and removing it, the
operation of inductively giving p a large positive charge
can be repeated again and again ; and we may thus
charge an insulated conductor with even a large capacity
to a high positive potential.
To save the trouble of having to electrically connect
p with B each time p is laid on the ebonite, it is desirable
(if an electrophorus is made simply for practical use and
not also for the purposes of instruction, as is the case
with the one shown in Fig. 137) to drill a hole through
the backing b (Fig. 138) and the
ebonite i, and insert a small brass
'^j^KKUUm^ screw s into it of such a length
J, j^ j^g that, when screwed in, its point is a
little below the upper surface of the
ebonite, for with this arrangement a spark passes
across the small air space when p is laid on the ebonite
in consequence of the high negative potential induced
in P ; but no spark passes on raising p, since its posi-
tive potential only becomes large when p is raised
so far from the ebonite that a spark cannot pass to
the screw. The presence, therefore, of this screw,
with its slightly countersunk point, has precisely the
same effect as connecting p with b when p is resting
* When the P. D. between two conductors reaches a certain value,
depending on their shapes, their distance apart, and the insulating
material separating them, a crack or hole is ifound in the insulator,
and a spark, produced by the burning of minute particles of the sur-
faces of the conductors, passes along the crack or hole. The P. D. re-
quired to produce a spark through air is given in § 196, page 370, but
for pflrafiined paper, guttapercha, glass, &c., it is much greater.
While the air is momentarily cracked, during the passage of a spark,
its resistance is comparatively small, but after the spark has passed,
the crack closes up, and the resistance regains its original value ; if,
however, the spark has passed through paper, a small hole may be
seen, differing, however, from a hole made by a pin, in that the former
is burred on both sides, as if the electric force making it had acted from
the centre of the paper outwards towards each side.
Chap. VII.] NEGATIVE CHARGES WITH ELECTROPHORUS. 359
on the ebonite, and removing this connection before p
is raised.
If it be desired to charge an insulated conductor of
large capacity to a high negative potential, we might use
an electrophorus with i (Fig. 137) made of glass, which
becomes charged j)ositively on being iiibbed with silk ;
but as glass is a much more hygroscopic body than ebonite,
and therefore much more difficult to keep electrified when
exposed to the air, it is better to use an ebonite electro-
phorus in the following manner.
193. Ebonite Electrophorus arranged to give Nega-
tive Charges. — Unscrew the handle from the plate p and
screw it into the back-
ing (Fig. 139). Excite
the ebonite by rubbing
it with cat's-skin, and
suppose that the back-
ing has been brought
to a potential nought
by connecting it for
a moment with the
ground when it was
held at some distance
from p, which is lying
on the table. The
ebonite is now the in-
sulated coating of a
condenser, the uninsu-
lated one being b and
the walls of the room.
Next holding the back-
ing and ebonite by the
insulating handle r,
place the ebonite on p
(Fig. 140). The po-
tential of the ebonite
will then become lef
will be raised to a high positive value, 'the density on
Fig. 139.
the potential of b
360
PRACTICAL ELECTRICITY.
[Chap. VII.
its upper side will become positive, the density on its
lower side less positive than before, and the density of
the upper surface of p positive. Connect b with p, the
potential of b will be reduced to nought, the potential of
the ebonite will be made still less negative, the density
on the upper surface of p made less positive, the density
on the upper surface of b nought, and on its lower sur-
face more positive than before.
Kaise the backing and the ebonite
by the handle, the potential of the
ebonite will become more negative,
and that of b will become negative
and will reach a high negative value
when the backing and ebonite are
removed some little distance from
p, so that a spark of negative elec-
tricity can be taken from b by a
conductor brought near it.
In the preceding we have
considered the various electrical
changes that take place on all the
parts of an electrophorus when in
use, but probably the simplest way
of looking at the action of the
electrophorus, whether it be used
Fig. 140. *o give positive or negative charges
to some conductor, is to remember
that when p is in contact with the ebonite plate, and
p and b are electrically connected together and with
the earth, there are charges of positive electricity on
the surfaces of p and b facing the ebonite, and these
charges may in each case be regarded as being due to
the excess of the inductive action of the negative charge
on the ebonite over that of the positive charge on the
other metal plate, the effect of the negative charge in
each case preponderating. Consequently if both p and B
could be separated from the ebonite by means of insu-
lating handles, both would be found to have a positive
Chap VII.l ACCUMULATING INFLUENCE MACHINES. 361
potential, and to be in a condition to give a positive
charge to some other conductor. And if the ebonite and
backing be removed without separation, p will, as before,
have a positive potential ; but the action on b will now
be qitite diferent from before, for, instead of the induc-
tive action of the positive electricity on p, together with
the preponderating inductive action of the negative
electricity on the ebonite, being removed simultaneously,
only the former is removed. Hence the inductive effect
on B of this negative electricity on the ebonite will pro-
duce an effect greater than before^ b will therefore have
a negative potential, and be in a condition to give a
negative charge to some other conductor.
In the electrophorus shown in the figures the ebonite
is held to the backing by three pins p p, instead of being
cemented to it as is usual in an electrophorus, and can
be removed by withdrawing these pins. Hence we can
examine the electrification of the ebonite or of the
backing in any stage of the experiments described above.
To charge a body of large capacity with a simple electro-
phorus is a slow process, and hence a *' rotatory electro-
phorus" h2i^ been devised by Bertsch for enabling the
operations described in § 192 to be rapidly performed,
but even this apparatus is inferior to the machines
described in the following sections.
194. Accumulating Influence Machines. — With the
electrophorus we can, as we have seen, increase the
potential of an insulated body until it is equal to that
of P, when p, with its induced charge in it, has been
removed far away from the ebonite, but we have no
means of increasing the charge in the ebonite itself;
and so, in order to use an electrophorus, it is necessary
to comriience by charging the ebonite by rubbing it with
a piece of cat's-skin. With an '* accumulating influence
machine" on the other hand, we are able to increase the
charge on the inductor, and hence to stai*t such a machine
with practically little or no charge on the inductor. The
action of all such machines depends on the folk wing prin--
362
PRACTICAL ELECTRICITY.
rChap. VII.
ciple : — If A and b (Fig. 141), be two insulated metallic
pots possessing a small P. D. between them, the potential
of A being the higher, and if C and d be two uncharged
conductors, c being placed near the outside of a, and d
Fig 141.
near the outside of b, the potential of c will be a little
higher than that of d ; hence if c and d be connected by
a piece of wire w, or other conductor, a small quantity
of positive electricity will flow from c to d, so that there
will be a small charge of positive electricity on d, and of
negative on c. If, now, the wire be disconnected from c
and D, and by means of insulating threads c be put in-
Chap. VII.] ACCUMULATING INFLUENCE MACHINES.
363
side B and be made to touch b near the bottom, while d
is put inside A, and is made to touch A near the bottom
(Fig. 142), the negative charge on c will be given up
entirely to b, and the positive charge on d entirely to A
(see § 64, page 118) j hence the P. D. between A and b
Fig. 142.
will be increased, c and d are now withdrawn, totally
discharged from B and A, and on being put again
into the position shown in Fig. 141, the operation is
repeated. If this be performed a sufficient number of
times, the P. D. between a and b may be made as large
as we like ; and as the charges induced in c and d depend
on the P. t>. already existing between a and b, it follows
364 PRACTICAL ELECTRICITY. [Chap. VII.
that the increase of P. D. goes on more and mere rapidly
according to the " compound interest lawP
195. Thomson's Replenisher. — An accumulating in-
fluence machine for rapidly performing the operations
Fig. 143.
described in the last section was devised by Sir "William
Thomson about 1867, and has been much employed.
The balls c and d, in Fig. 141, are replaced by two gilt
brass " carriers " c, d, seen in perspective in Figs. 143, 145,
and in plan in Fig. 144. These are carried eccentrically
at the ends of an ebonite rod r, fixed to an ebonite
spindle e, and by turning this spindle by means of the
milled head m at the top (Fig. 145), the carriers are
rapidly carried round. The metal pots A and b, of Fig. 141,
Chap. VII.]
THOMSON S REPLENISHER.
365
become the gilt brass "inductors" ab (Figs. 143, 144,
145), and the wire w is replaced by two springs s s', con-
nected by a strip of brass M fixed round the edge of the
piece of ebonite p. This ebonite carries the springs and
also the end of the spindle, and is itself supported as seen
in Fig. 1.45. When the carriers C d simultaneously touch
Fig. 144.
the springs s s', they are practically in the same electric
condition as are c and d (Fig. 141), and are acted on
inductively by the charges in the inductors A b ; while,
on the other hand, when they have been turned round
further in the direction of the arrow (Fig, 144) until they
touch the springs s' 5, which are connected respectively
with the two inductors, the carriers are electrically in the
same condition as are c and d (Fig. 142) — that is, they
are under cover of the inductors, and so part with their
charges to these inductors.
It is found that there is alwaysi a sufficiently large
366
PRACTICAL ELECTRICITY.
[Chap. VII.
P. D. between the inductors ab (Fig. 143), no matter
how well they may have been previously discharged, to
start the action of the " ThomsorCs replenisher,^ and to
enable the apparatus (if it be well constructed, and also
clean and dry) to rapidly produce sparks on the compound
interest principle.
To prevent the carriers C d causing the inductors A b
to lose electricity by
being left in contact
with them, or by being
electrically attracted
round so as to come
into contact with them,
when the replenisheris
not in use, the milled
head m (Fig. 145) is
fixed in the position
seen in this figure by
a pin attached to the
farther side of the
square head h, fitting
into a hole in the head
M. On turning the
head h, this pin is
withdrawn from the
milled head m, which
is then free to turn,
and the spring k press-
ing against the square
rig. 145. head n is for the pur-
pose of holding the
head in one or other of two definite positions — in one
of which the pin locks the milled head m, and in the
other leaves it quite free.
The earliest machine in which this compound interest
principle of electrophoric action was used, was the " re-
volving douhler^^ in\QYitQd by Nicholson more than one
hundred years ago. This apparatus, ho\\'ever, seems to
Chap. VII.] WIMSHURST INFLUENCE MACHINE. 367
have remained practically unknown, and unused. In
1860 0. F. Varley invented a somewhat similar appa-
ratus, and still later a well-known machine was devised
by Holtz, which, however, required an initial P. D. to
be set up between the inductors by a piece of rubbed
ebonite in order to start the action. So far the Holtz
machine resembles the electrophorus, but while in a
simple electrophorus, or even in Bertsch's rotatory elec-
trophorus, there is no contrivance for even maintaining
the P. D. between the inductors, the Holtz machine
is so designed that the P. D. is increased by the action
of the machine. This machine differs, however, from
Thomson's replenisher : first, in that the carriers are
practically infinite in number ; secondly, in the connect-
ing wire w (Figs. 141, 142), and s s' (Figs. 143, 144),
having a break in it so that it is divided into two parts,
and the P. D. that is set up between these two parts when
any pair of carriers are simultaneously in electrical contact
with them, being the P. D. that is practically made use of.
The next improvement was made by Voss, who pro-
duced an accumulating influence machine which com-
bined the advantages of the Thomson's replenisher and
of the Holtz's machine, in that it required no initial
P. D. to be given to the inductors to start the action, and
produced considerable quantities of positive and negative
electricity for an influence machine. It is, however, un-
necessary to describe either this or the Holtz machine in
detail, because the latest accumulating influence machine
constructed by Mr. Wimshurst is not only extremely
simple in construction, but is probably the most perfect
machine of this type that has yet been devised.
196. Wimshurst Influence Machine. — This machine
consists of two circular discs of ordinary window glass
(Fig. 146), each attached to the end of a hollow boss of
wood, or ebonite, upon which is turned a small pulley.
These bosses are mounted on a fixed horizontal steel
spindle, so that the glass discs are about one-eighth of an
inch apart, and are rotated in opposite directions by the
368 PRACTICAL ELECTRICITY. [Chap. VIL
cords which pass over the pulleys at the base of the in
strument, one of the driving cords being crossed for this
purpose. The glass discs are carefully coated with shell-
lac varnish, and on the outside of each of them there are
cemented an equal number of radial, sec tor- shaped plates of
Fig. 146.
thin metal at equal distances apart, which act the part not
only of the carriers CD (Figs. 143, 144, pages 364, 365),
but also of the inductors a b, the carriers on one disc
acting as the inductors for the carriers on the other. If
only ten sectors be stuck on each of the glass discs, it is
found that the machine will only excite itself under very
favourable circumstances, whereas if there be sixteen or
eighteen, it will excite itself under all atmospheric con-
ditions. Two curved brass rods, terminating at their
Chap. VII.] WIMSHURST INFLUENCE MACHINE. 369
ends in fine wire brushes, are placed, as seen in the
figure, one at the front of the machine, and one at the
back, making an angle of about 90° with one another,
and about 455 with the horizontal " collecting combs."
These rods act like the springs s s' (Figs. 143, 144) in con-
necting a pair of carriers when they are under the induc-
tive action of the inductors, which in this machine are
the adjacent carriers on the other plate. The combs are
four in number, two being placed at the front of the
machine, as seen in the figure, and two at the back, the
points of the combs being directed towards the discs.
The two combs at the left hand are connected together,
and form one terminal of the machine, while the two at
the right hand form the other. These combs are sup-
ported in position by the brass cylinders to which they
are attached, and which stand on glass legs. These
cylinders carry the two " discharging rods " which
terminate in two balls, and in order to charge any two
bodies (the inside and outside of a Ley den jar, for ex-
ample) to a high P. D., they must be connected with
pieces of wire to the brass cylinders, and the balls at the
ends of the discharging rods separated.
It does not appear that the collecting apparatus takes
any important part in the inductive action of the Wims-
hurst machine, for if it be removed and the glass discs
made to spin round in opposite directions, their whole
surface is seen to glow with a luminous discharge, and a
sharp crackling sound is heard. The collection of the
positive and negative charges might be effected by attach-
ing springs to the horizontal rods so as to touch the car-
riers as they pass instead of using the combs which collect
by a " brush* discharge," but the combs introduce, of
course, far less frictional resistance to the motion of the
plate, and act very well, because when a carrier comes
* If the P. D. between two conductors be raised, it is found that
before it reaches the value that will cause a spark to pass between
the conductors, a hissing sound is heard, and a '^ brush" or "gloio
discharge " takes place, rendering the space between the conductors
luminous in the dark.
Y
370 PRACTICAL ELECTRICITY. [Chap. VIL
between a pair of combs, it is practically inside a con-
ductor ; and we have seen that when a body is inside a con-
ductor, no charge that the conductor may have can prevent
the body discharging itself into the conductor, and as,
in addition, the density is very great at a point (see § 63,
page 118), the charge easily passes across the small air
space separating tlie points of the teeth of the comb
from the surface of a carrier when it is passing the comb.
Hence, in all modern frictional or influence machines,
such combs have been used as the collectors.
By attaching the inner coatings of Leyden jars to the
sets of collecting brushes, the outer coatings of the jars
being connected together, the capacity of the collectors
is much increased, hence the brightness of a spark and
the noise that it makes in passing from one of the balls
to the other is also much increased. As, however, we
cannot augment the rate of work done by the machine in
this way, and as the work given out by each spark
equals
foot lbs.,
2-712
{see § 176, page 323), where F is the capacity in farads of
one of the Leyden jars that is discharged, and Y the
P. D. between their inner coatings, it follows that for a
given influence machine and for a given rate of turning,
the rapidity of producing sparks will be diminished by
connecting Leyden jars with the collecting combs.
The P. D. produced between the terminals of an in-
fluence machine can send a spark from one of the balls
to the other when they are separated by a distance of
several inches. When the surfaces of two metallic balls
are separated by more than about one-tenth of an inch,
the experiments made by Drs. De la Rue and Hugo
Miiller, show that the P. D. required to produce a
spark is nearly proportional to the distance between
their surfaces, and increases at the rate of, roughly,
10,000 volts per one-tenth of an inch, so that it
Cliap. VII.] VARIATION OF STRIKING DISTANCE WITH P.D. 371
would require a P. D. of about 100,000 volts to start
a spark between two metal balls separated by a distance
of one inch. If the bodies between which the spark
passes be a point and a plate, the " striking distance "* is
greater for the same P. D., being at the rate of one inch
for every 23,400 volts P. I), between the point and the
plate. From this it will be seen that an influence
machine can produce a P. D. between its terminals of
some hundreds of thousands of volts ; consequently,
the quantity of electricity that passes in the sparks must
be very small, since the work, in foot pounds, done per
minute by the machine, equals
44-25 A V,
{see § 114, page 201), where A is the mean value in
amperes of the current passing, and V the mean P. D. in
volts between the terminals, and this product cannot ex-
ceed about 5,000, the greatest work, in foot pounds per
minute, that a man can do in turning the machine. Hence,
although brilliant sparks and powerful shocks can be pro-
duced with such a machine, we cannot expect that it
will produce any visible decomposition in a voltameter
used to join its terminals, or that it will cause a de-
flection of the needle of even a sensitive galvanometer.
A galvanic cell of small resistance can produce a cur-
rent of many amperes through a small external resist-
ance, and yet can only produce a maximum P. D.
of a volt or two, whereas an influence machine is, to a
certain extent, like a very large number of cells. in series,
each cell having a very high resistance, for such a bat-
tery can produce a very high P. D. between its terminals
* The striking distance is the distance that separates two conduc-
tors when a spark is started between them. To maintain a continuous
"' electHc arc ' between two conductors requires a much smaller P. D.
than to start a spark between them ; for example, to maintain an arc
one inch long between two carbon rods only requires a P. D. of about
118 volts if the carbons be hard, and a less P. D. if they be soft. (See
y The Resistance of the Electric Arc. " Phil Mag. , May, 1883.) Hence
in all " arc lamps " there must be some mechanism for first bringing
the carbons into contact, to start the arc, and then separating them.
372 PRACTICAL ELECTRICITY. [Chap. VII.
if they be insulated, but only a very weak, steady current,
even if its terminals be joined together with a short
thick piece of wire, and the battery short-circuited.
The low resistance cell is in fact analogous with a large
shallow reservoir of water which is constantly kept filled
with a big supply tap, while an influence machine with
the balls at some distance apart is analogous with a very
tall, very narrow tube, into which water slowly but
steadily trickles. If a tap at the side of the former be
opened and left open, there will be a large, steady stream
of water, but the distance through which the stream will
spurt from the side of the reservoir will he small , whereas
if a tap at the side of the tall, narrow tube, near the
bottom, be opened, the water will spurt out through a
distance of many feet, but the stream will rapidly fall off
as the tube empties, and the spurt can only be repeated
by keeping the tap at the bottom of the tube closed,
while the tube is refilling.
The distance at which the balls of an influence
machine are separated, determines the maximum P. D.
that can be set up between the discharging rods, or be-
tween any two conductors connected with them ; hence,
by placing the balls at a given distance apart, and then
turning the machine until a spark is just going to pass
between them, we know approximately the P. D. set up
between two conductors connected with them.
197. Dry Pile. — When it is desired to maintain a
high P. D. between two conductors that are well insu-
lated from one another, as, for example, the outside of
an electrometer, and the needle inside {see § 75, page
130), a battery consisting of a large number of cells in
series, each cell having a high resistance, may be em-
ployed, since, as the resistance external to the battery is
infinite, the P. D. at its terminals will be simply the
E. M. F. of the battery, no matter how high may be the
resistance of each cell. Fig. 147 shows a section of such
a battery, consisting of a large number of small, simple
voltaic elements, joined up in series. The liquid part
Chap. VII.1 DRY PILE. 373
of each cell may be made smaller and smaller without
affecting the P. D. at the terminals of the battery, pro-
vided that it is not required to send any current, and it
may be reduced to simply the moisture which exists in
ordinary paper when exposed to the air. In that case
the zinc and copper plates may be pieces of metallic foil
stuck on to the two sides of each piece of paper, or the
cell may be formed simply of a piece of paper with a
little powder rubbed on each side. In Zamboni's con-
Fig. 147.
struction of a dry pile, sheets of paper' are prepared by
T^di.simg finely laminated zinc or tin on one side, and rub-
bing manganese peroxide, or what is sometimes called
black oxide of manganese, on the other. Discs are punched
out of this paper, and several hundred of them are piled
up into a column, with their similar sides all facing the
same way, inside a glass tube tt (Fig. 148), which has
been carefully coated inside and out with shell-lac
varnish. The discs are kept in contact with one another,
and electric connection is made with the two outside ones
by their being pressed between the brass plate p and
the brass cap b, cemented to the bottom of the tube.
The plate p is pressed down by the wire w, which is held
374
PRACTICAL ELECTRICITY.
[CLap. VII.
in position by a sraall pinching screw s (Fig. 149), which
fixes it in a collar c soldered to the inside of the other
brass cap A, which latter is cemented to the tube at the top.
The dry pile may be conveniently hung by one of its
terminal wires from the outside of the Edelmann electro-
Fig. 148.
Fig. 149.
meter seen in Fig. 48, page 132, and its lower wire con-
nected with the wire j^ of the electrometer. Although
the pile will bring any two insulated bodies attached to its
ends to a fixed P. D., its resistance is too high to enable
it to instantly supply the electricity necessary to do this if
the capacity of one of the bodies be suddenly changed,
therefore, to avoid the capacity of the brass end of the
Chap. VII. ] ELECTROMETER CHARGED WITH PILE. 375
pile, which is electrically connected with p, being suddenly-
increased by some conductor in connection with the earth
being brought near it, which would have the effect of
momentarily lowering the potential of this end, and there-
fore of the electrometer needle attached to it, it is desir-
able to enclose the pile in a brass tube ^ ^ of somewhat
larger diameter than the glass one, and to support the pile
inside this metal ^^ guard tube." This may be done by
fixing the end of one of the terminal wires by a pinching
screw 5 to a collar c, soldered to the outside of the end of
the guard tube as seen in section in Fig. 149. The brass
cap B at the bottom of the pile forms a condenser of
fixed capacity with the brass tube, and must not, of course,
even momentarily, touch this tube. The whole apparatus
may then be conveniently supported from the outside of
the electrometer, by placing a lug L projecting from the
metal top of the guard tube, under the clamping nut N
of one of the levelling screws of the electrometer (Fig. 149).
A dry pile is much more simple and compact than a
battery, consisting of some hundreds of cells, but expe-
rience shows that when considerable accuracy is desired,
it is better to use some form of battery (such as that
illustrated in Fig. 147, for example) than a dry pile to
keep the electrometer needle charged.
M>^
praScc^ ^^
376
CHAPTER VIII.
COMMERCIAL AMMETERS AND VOLTMETERS.
198. Detect of Permanent Magnet Meters — 199. Siemens' Electro-
Dynamometer — 200. Cunynghame's Ammeter and Voltmeter —
201. Instruments with Magnifying Gearing — 202. Magnifying
Spring Ammeter and Voltmeter — ^03. Gravity Control Meters —
204. Crompton and Kapp's Meters — 205. Paterson and Cooper's
Electro-magnetic Control Meters — 206. Testing Ammeters — 207.
Test for Accuracy of the Graduation — 208. Test for Residual Mag-
netism— 209. Test for Error on Reversing the Current — 210. Test
for Error Produced by External Magnetic Disturbance — 211. Test
for Permanent Alteration of Sensibility — 212. Testing Voltmeters
— 213. Test for Accuracy of the Graduation — 214. Latimer Clark's
Cell— 215. Standard Darnell's Cell— 216. Test for Heating Error
— 217. Variation of the Sensibility of a Galvanometer with its
Resistance — 218. Rate of Production of Heat in Galvanometer
Coils— 219. Standard Voltmeter— 220. Cardew's Voltmeter— 221.
Commutator Ammeter and Voltmeter — 222. Calibrating a Com-
mutator Ammeter — 223. Calibrating a Commutator Voltmeter
— 224. Best Resistance to Give to a Galvanometer.
Commercial instruments for the accurate direct measure-
ments of amperes and volts are quite as important as
boxes of resistance coils accurately graduated in ohms ;
but while the construction of resistance coils has engaged
the attention of manufacturers for the last twenty years,
it is only since about 1880 that the construction of com-
mercial ammeters and voltmeters has been considered.
This, combined with the fact that it is far more easy to
construct a coil of wire that will have a perfectly con-
stant resistance at a fixed temperature, and even a fairly
constant resistance within a considerable range of tem-
perature, than a measuring instrument that will be con-
stant in its indications, makes it desirable to devote a
chapter to commercial ammeters and voltmeters.
198. Defect of Permanent Magnet Meters. — The
ammeters and voltmeters described in §§36, 72, pages
73 128, have the disadvantage that, if they be placed too
near a large powerful magnet, such as a dynamo machine
Chap. VIII.] SPRING CONTROL METERS. 377
or an electromotor, not only is the strength of the con-
trolling ^eld, and consequently the sensibility of the in-
strument, temporarily varied, but the permanent magnet
of the ammeter, or voltmeter, may have its magnetism
permanently altered, in which case the sensibility of the
instrument will also be permanently altered without the
user being in many cases aware that any such change has
taken place.
To avoid the possibility of this very serious error
arising, the permanent magnet must be dispensed with,
and the controlling force produced in some other way.
Three forms of controlling force not produced by perma-
nent magnets have been made use of, namely : —
1. The pull of a spring ;
2. The attraction of gravity ;
3. The attraction of an electro-magnet temporarily
magnetised by the whole or a portion of the current to
be measured.
Spring Control Meters.
199. Siemens' Electro-Dynamometer. — Probably the
oldest form of commercial current measurer, employing
a spring to produce the controlling force, is ^^ Siemens^
electro-dynamometer^^^ shown in perspective in Fig. 150,
and. symbolically in Figs. 151 and 152. It consists of a
fixed coil A BCD (Fig. 151), and a movable coil E f g,
which latter is frequently made of a single stiff wire. The
current passes round the fixed coil and through the
movable coil or wire in series, electric connections with
the two ends of the latter being maintained by their dip-
ping into mercury cups mm! (Fig. 151).
The movable coil is suspended by a thread and by a
delicate spiral spring n (Fig. 151), which latter can be
twisted by turning the milled head t (Figs. 151 and 152)
through an angle, which is measured by the pointer m
attached to the head t, turning over a scale gradu-
ated in degrees, or, instead, in 400 equal divisions,
and seen in Fig. 152. The instrument having been
378 PRACTICAL ELECTRICITY. [Chap. VIII.
levelled by means of the plumb-line, seen to the right
of Fig. 1»W, the head t is turned until the plane of the
movable coil e f g is at right angles to that of the fixed
coil A B c D, which is indicated by the pointer P attached
to the movable coil (Figs. 151 and 152) coming opjDOsite
Fig. 150.
the 0'^ on the dial. Should the pointer m not now also
point to the 0°, a small pinching screw which clamps
the pointer m to the head T is loosened, and m is turned
to the 0° without turning the milled head t, or twisting
the spring n. If a current be sent through the instru-
ment entering at the left-hand binding screw (Fig. 151),
and following the path ABCDmEFG m', and leaving
Chap. VIII.] SIEMENS ELECTRO-DYNAMOMETER.
379
therefore by the right-hand binding screw, the movable
coil turns, tending to place its plane parallel with
that of the fixed coil, until the pointer p comes up
against the right-hand stop s (Fig. 152). On turning the
head t, and the pointer M attached to it, through an angle,
say, of 50°, p can be again brought to 0°. The couple
exerted between the coils is balanced by the couple
exerted by the twisted spring, and the moment of the
Fig. 151.
latter is proportional to the angle through which m has
been turned.
To compare the current now passing through the
dynamometer with some other current, exactly the same
adjustment is made when the other current is passing,
and since the movable wire, or coil, is always brought
back to the same positio7i relatively to the fixed one, the
couple exerted between the coils is proportional simply
to the product of the current passing through one coil
into the current passing through the other — that is, to
the square of the current passing through them in series.
Hence, the angle through which m has to he turned from
380 PRACTICAL ELECTRICITY. iChap. VIIL
the zero position to bring the pointer P to 0°, is propor-
tional to the square of the current.
In the actual instrument, as seen in Fig. 150, there
are two fixed deflecting coils having a different number
of convolutions, and either of which can be employed
by using the middle and the right-hand binding screw, or
the middle and the left-hand one. The two coils have
usually the one about five times as many convolutions as
the other, so that the sensibility of the instrument when
using the one is about five times as great as when using
the other.
The advantages of this instrument, in addition to the
one already mentioned that it contains no permanent
magnet, are : — First, since the fixed and moving parts
between which the electric attraction is exerted always
occupy exactly the same position relatively to one another
when an observation is being made — that is, since the
dynamometer is a ^^ zero instrument " — one experiment is
all that it is necessary to make to enable the graduation
of the whole scale to be effected with great accuracy,
since the law of the instrument is known exactly, arising
from the fact that as long as two wires occupy exactly
the same relative positions the force exerted by each on
Chap. VIII.] SIEMENS* ELECTRO-DYNAMOMETER. 381
the other is directly proportional to the product of the
currents passing through them respectively ; second, this
dynamometer can be used with, considerable accuracy to
measure an alternating current — that is, one the direc-
tion of which undergoes rapid reversals, since the direc-
tion of the current in both the moving and stationary
coils will be reversed simultaneously, and the force be-
tween them will therefore remain the same as before the
reversal.
The disadvantages of the Siemens' dynamometer are :
— First, the instrument being one in which the moving
coil has always to be brought to zero, cannot show at
once, without adjustment, the strength of a current, and
as a little time is necessary to enable this adjustment to
be made, the instrument cannot be used for measuring
sudden variations in the strength of a current ; second,
owing to the moment of inertia of the suspended coil
being rather large, the instrument is not dead-beat ;
third, the readings are much affected by neighbouring
magnets, or wires conveying currents ; indeed, the wires
leading the current into and out of the dynamometer
must be carefully twisted together, so that their mean
distance from the moving coil may be the same, and the
action of the current in the one leading wire balanced by
the action of the equal and opposite current flowing in
the other ; further, as the suspended coil when traversed
by a current is acted on by the earth's magnetism, the
instrument must always be placed so that the plane
of the suspended coil^ when p is at 0°, is at right angles to
the plane of the earth! s magnetic meridiccn, since this is
the position in which the coil desires to place itself as
far as the action of the earth's magnetism is concerned
when a current is passing through it ; fourth, as the
instrument must be placed in this particular position
before use, also as it must be levelled and mercury poured
into the cups m and m' (Fig. 151) if it has been spilt
when the instrument is carried about, it is not very
portable ; fifth, the movable coil being quite uncovered,
382 PRACTICAL ELECTRICITY. [Chap. VIII.
is blown about by draughts of air, and the spring is
liable to be accidentally damaged by things being knocked
against it ; sixth, the scale, being graduated in degrees,
or arbitrary divisions, is not direct-reading ; and lastly,
the instrument gives no indication of the direction of
the current^ which, in electroplating, electrotyping, the
charging of accumulators, &c., is as important as the
strength of the current.
Shortly, therefore, we may say that the Siemens'
dynamometer is an extremely valuable standard instru-
ment when it can be kept and used in Sijlxed position in
a laboratory far away from all moving magnets, or wires
in which strong currents are passing, &c., and its con-
stant experimentally determined in that fixed position ;
but for a portable instrument to be carried about in a
workshop or room containing dynamos in motion, and
used wherever required, there are other instruments
more convenient.
200. Cunynghame's Ammeter and Voltmeter. —
These zero instruments are a modification of the Siemens*
dynamometer, an electro-magnet ee (Fig. 154) being
substituted for the stationary deflecting coil, and a
pivoted soft iron needle N (Figs. 153 and 154) for the
movable one, the magnetic axis of the needle, as seen
in Fig. 153, which shows a sectional plan of the in-
strument, making an angle of about 30° with the line
joining the poles p p of the electro-magnet, when a
pointer attached to the moving needle is at 0°. The
soft iron core c c of the electro-magnet, seen in sectional
elevation in Fig. 154, is made massive, in order that a
considerable magnetic force may be produced by it for a
comparatively small magnetic action of the current, be-
cause experiment shows that when the core of an electro-
magnet is only slightly magnetised, the strength of the
magnet is directly proportional to the current, the strength
of the magnet being measured by the force with which it
attracts or repels one end of a hard steel permanent
magnet, put in a given position relatively to the electro-
Chap. VIII.]
CUNYNGHAME S METERS.
383
magnet ; whereas if the magnetic action of the coil be
great, the soft iron core becomes " saturated^^' and its
Fig. 153.
strength hardly increases with an increase in the current.
The soft iron needle is magnetised inductively by the
electro-magnet, *and for a given relative position of the
384
PRACTICAL ELECTRICITY.
[Chap. VIII.
two the amount of magnetism induced in the iron needle
will be directly proportional to the strength of the electro-
magnet, provided the needle is so massive that it is far
from being ''saturated" {see page 388). Under these cir-
cumstances the couple exerted by the electro-magnet on the
needle will be proportional to the square of the current.
Fig. 154.
This couple is balanced by the twist given to the spiral
spring, as in the Siemens' dynamometer, and therefore is
also proportional to the angle through which the pointer m,
attached to tlie milled head t, has been turned. As long,
therefore, as we are dealing with currents not strong enough
to saturate the iron core and the iron needle, the angle
through which the pointer attached to the milled head has
to be turned to bring the pointer attached to the moving
needle to 0° is proportional to the square of the current.
Chap. vin.i cunynghamr's meters. 385
The scale is, therefore, graduated not in degrees, but in
numbers proportional to the square roots of the number
of degrees, and the adjustable pole-pieces p p enable the
instruments to be made direct-reading {see § 37, page 76).
The wires leading the current to and from the instrument
are fastened to the binding screws bb (Fig. 153).
The advantages of this type of instrument are : —
First, the controlling force not being produced by a per-
manent magnet, the sensibility cannot be permanently
changed by placing the instrument near a powerful
magnet ; second, its indications are but little affected by
an outside magnet, as the mass of soft iron in the core
and pole-pieces of the electro-magnet shields the needle
to a great extent from external magnetic disturbance {see
§ 52, page 102) ; third, it is direct-reading ; fourth, it is
dead beat ; fifth, it has no mercury cups, does not require
levelling, can be used in any position, is not likely to be
damaged, as the pointers and spring are all boxed in ;
and hence the Cunynghame instruments are very portable.
The disadvantages are : — First, being a zero instru-
ment, an adjustment has to be made before the value of a
current can be read, and therefore the magnitude of sudden
changes in a current cannot be measured ; second, it can
only be used to measure currents in one direction ; third,
in spite of the mass of iron the current is not quite pro-
portional to the square root of the angle, and therefore
the reading is a little too small for large currents {see
§208, page 401); fourth, in consequence of ^^ residual
magnetism,"* the value of a current corresponding with
a particular reading depends somewhat on whether the
currents previously passing through the instrument were
larger or smaller than the one being measured {see § 208,
page 401) ; fifth, in consequence also of residual magnetism,
a reverse current sent for a short time through the
* y Residual magnetism" is the name given to the magnetism that
remains in a substance after the magnetising force has ceased. With
very soft iron the amount of residual magnetism is small, whereas
with hard steel it is very large.
Z
386 PRACTICAL ELECTRICITY. [Chap. VIII.
instrument diminishes the subsequent indications for small
direct currents (see § 209, page 403).
Shortly, therefore, we may say that while the instru-
ment has not an exact law, and cannot, therefore, like a
Siemens' dynamometer, be used as a standard instrument,
it is far more convenient for general use in the workshop
and in an electric lighting establishment. ^
201. Instruments with Magnifying Gearing. — We
have seen (§ 20, page 46) that if all the deflections of a
galvanometer are small, the deflections will be directly
proportional^o the current whatever be the shape of the
coil and needle ; hence, attempts have been made by M.
Deprez to use a form of portable current galvanometer,
in which the needle could only deflect through a small
angle, and to magnify this deflection by attaching the
pointer to a small grooved pulley geared by a fine end-
less thread to a much larger grooved wheel attached to
the needle. A similar result has been attained by the
author by using instead of the small and large grooved
wheels a small toothed wheel, or pinion, attached to the
pointer, and a larger toothed wheel to the axle or stafl" of
the needle. Such contrivances, however, for magnifying
the motion by means of pivoted gearing cannot be recom-
mended, as they introduce friction as well as add to the
moment of inertia of the moving parts, and so diminish
the dead beat character of the apparatus. These diffi-
culties, however, have been overcome in the following
apparatus : —
202. Magnifying Spring Ammeter and Voltmeter.
— In these instruments, devised by the author, a special
form of spring is employed, shaped like a narrow shaving
curled up into a cylinder of very small diameter (Fig.
155). Such a spring, quite unlike an ordinary spiral
spring, has the peculiarity that for a small increase in
length along the axis there is large rotation of one end of
the spring relatively to the other, the angle of rotation
being directly proportioned to the axial extension. Hence,
if one end of the spring be fixed and the other be slightly
Chap. VIII.]
MAGNIFYING SPRING METERS.
387
pulled axially, a pointer attached to this end will turn
through a large angle, and so will measure in a very
magnified way the axial extension of the spring, without
the employment of a rack and pinion, or of levers, or of
any other magnifying arrangement,
and without, therefore, the cost or
the friction attending the use of
such magnifying arrangements.
The instrument is shown in Fig.
lo6, where tt is a thin tube of
cliarcoal iron, attached at its lower
end to a brass cap c, terminated in
a brass pin Pj guided at the bottom
in the way shown. To C is attached
the lower end of the spring s (made
of hard phosphor-bronze), the upper
end of which is attached rigidly to
a brass pin ^^, passing through a hole
in the glass top of the apparatus
GG, and fastened by means of a
screw and nut to the brass milled
head h outside the glass top. This
pin /?, to which the upper end of the
spring is attached, also serves as a
guide to the top of the iron tube.
In the space vv w a ^^ solenoid^' * wire or strip is wound,
its ends being attached to the terminals shown. Hence,
when a current is passed through this solenoid, the iron
tube is sucked down into the solenoid, and its lower end
c, to which the spring is attached, receives a large
rotatory motion, which is communicated directly to the
pointer attached to the top of the iron tube. Parallax,
in taking readings of the pointer, is avoided by the
horizontal scale having a piece of looking-glass let in it
in the well-known way. (See § 12, page 28.)
By making the iron tube t t very thin, so that . it is
* A coil of wire wound as cotton is on a reel, is called a " solenoid '*
when the length of the coil is not small compared with its diameter.
Fig. 155.
388
PHACTICAL ELECTRICITY.
[Chap. VIII.
^^magnetically saturated" for a comparatively weak cur-
rent— that is, so that a current passing round the coils
much weaker than the instrument is intended to measure
Fig. 166.
is able to impart to the iron as much magnetism as it is
possible for any current to give to it — also by fixing the
iron tube so that it projects into the solenoid a definite
distance, which has been carefully determined, partly by
calculation and partly by experiment, and lastly by con-
structing the spring so as to produce a large rotation
Chap. VIII.] MAGNIFYING SPRING METERS. 389
with the minimum pull, and with not too much axial
motion of the free end of the spring, deflections up to
270° can be obtained directly proportional to the current^
excepting for the first 15°, where the scale is not gra-
duated.
This instrument being direct-reading has to be pro-
vided with an adjustment for sensibility, and this is ob-
tained partly by the amount of wire or strip that is
wound on the bobbin, and partly by means of a small
movable bobbin, wound with a coil of fine wire of the
same length as that employed in winding the main coil,
joined up in parallel with the main coil. This movable
coil slides up and down on the main bobbin, and by
trial a position is found for it such that the readings
on the dial are correct, and in that position this
auxiliary coil is permanently fixed by the maker of the
instrument.
The pointer will deflect in the same direction, no
matter which way the current passes through the in-
strument, and owing to the softness of the iron used in
making the tube T T, and the smallness of its mass, there
is but very little residual magnetism left in it ; hence
the pointer indicates the correct strength of the current,
no matter which way it passes through the instrument.
To ascertain the direction of the current, a small compass
needle is let into the base of the instrument, as seen in
Fig. 156, which is deflected when the current passes
through the instrument in such a way, that when the blue-
coloured end of the compass needle points inwards, the
current enters at that one of the binding screws that
has an A marked on it, the nearer binding screw in this
figure.
As, however, experience shows that the compass needle
may have its magnetism reversed by a sudden very strong
current sent through the ammeter (in spite of the needle
being surrounded by iron to partially shield it from the
action of the current), and as, in addition, its position can-
not be very easily seen by an observer unless close to the
390 PRACTICAL ELECTRICITV. [Chap. VIH.
instrument, the direction of the currents in the latest
magnifying spring instruments is indicated by a much
larger magnet, suspended on a horizontal axis in front
of the instrument, which points to the binding screw
at which the current enters.
The advantages of this instrument are : — First, owing
to the controlling force not being produced by a perma-
nent magnet, the sensibility of the instrument cannot be
permanently affected by placing it near a powerful mag-
net j secondly, the sensibility will not be even temporarily
affected, no matter how strong this outside magnet may
be, provided that it is so far away that the magnetic field
is uniform throughout the small space in which the little
iron tube tt moves {see § 15, page 36). For example,
although an ordinary compass needle is turned round by a
uniform magnetic field, there is no force tending to pull the
compass needle bodily along, as may easily be proved by
floating a compass needle on a piece of cork in a basin of
water, when it will be found that while the needle will
place itself at once so that its axis points north and south,
it will not move towards the side of the basin as it would
if it were pulled as a whole in some direction. Or the
experiment may be tried thus : — suspend a bar of unmag-
netised hard steel by one of its ends from the pan of a
delicate balance, so that the bar hangs vertically down-
wards, and weigh it, then magnetise the bar, and
weigh it again, when it will be found that its weight is
neither increased nor diminished in the slightest by the
magnetic action of the earth. This fact is expressed by
saying that a uniform magnetic field can produce a
motion of rotation, hut not a motion of translation of a
magnet. Now, the magnet that is moved in the magni-
fying spring instrument is the soft iron tube t t, which
has a north-seeking pole induced on its lower end, say,
and a south-seeking pole on its upper end, or vice versdy
by the current passing round the coil of wire or strip,
and this tube is simply pulled downwards by the
attraction of the current passing round this coil. Hence,
Chap. VIII.] GRAVITY CONTROL METERS. 391
this pulling action is neither increased nor diminished by
the magnetic action of the earth, nor by the action of
any magnet, no matter how strong it may be, if the field
it produces is uniform over the space in which the iron
tube moves ; second, by using the magnification introduced
by the special form of spring, the distance moved through
by the attracted iron tube is not large, so that the in-
strument has much of the advantage of a zero instrument
{see § 199, page 380), that is, the force depends simply
on the current, and is practically unaffected by the
motion of the attracted soft iron tube. This, combined
with the small mass of iron, causes the increase of force
to he directly proportional to the increase of current. The
scale is therefore long, and the distances corresponding
with a given fraction of an ampere or of a volt are
equal throughout the whole length of the scale, which
not only facilitates the manufacture of the scale, but
greatly increases the power of estimating by eye
the decimal parts of a division. Hence, a current, or
a P. D., can be read to a very small fraction of its total
value.
The main disadvantage of the instrument is that
currents or P. Ds. less than about one-fifth of the
maximum current or P. D. that the instrument is in-
tended to be used for cannot be measured, since for
currents under this value the iron tube is not mag-
netically saturated.
Gravity Control Meters.
203. Gravity Control Meters. — Instruments in
which the controlling force is produced by a weight at-
tached to the needle have been devised by Sir William
Thomson, Messrs. Schuckert, Edelmann, Statter, and
others.
j The advantages of such instruments are : first, as the
'controlling force is absolutely constant, the sensibility ol
392 PRACTICAL ELECTRICITY. [Chap VIIL
the instrument cannot vary from time to time on account
of a variation in the force; second, the price is low,
arising from the simplicity of construction.
The disadvantages are : first, the readings usually are
easily varied by extraneous magnetic disturbance ; second,
there is generally a certain want of quickness of action,
so that any small temporary change in the strength of the
current or P. D. that is being measured is not instantly
recorded. For this purpose the needle and pointer must
not only be veiy light, but the controlling force must be
great {see § 38, page 78). Now, if gravity be used, the
only way to obtain a large controlling force is to use a
large mass to be attracted, but if a large mass be
attached to the needle and pointer, the moment of inertia
will be seriously increased, and slow motion will be the
result ; whereas, by using a powerful controlling magnet
or a comparatively strong spring, we obtain a dead-beat-
ness so great that the number of times the joint in the
driving-belt passes over the dynamo pulley can be easily
counted, every adjustment in the carbons on an arc lamp
be seen on the ammeter and voltmeter, and even the effect
on an arc lamp produced by whistling may be instantly
observed on the distant ammeter.
The gravity control meters of Sir William Thomson
not yet being in common use, the author has had no ex-
perience with them, and, therefore, cannot speak of their
advantages or disadvantages.
Electro-magnetic Control Meters.
R04. Crompton and Kapp's Meters.— The third de-
vice, which consists in using for the controlling force that
produced by an electro-magnet, round which flows the
whole or a portion of the current to be measured, appears
at first sight to be the best ; but it is attended with very
serious practical difficulties. The possibility of using a
current to deflect a needle, and the very same current to
Chap. VIII.] ELECTRO-MAGNETIC CONTROL METERS. 393
resist its being deflected, without obtaining the same de-
flection for all currents (a result which would occur if the
deflecting and controlling forces varied proportionally to
one another as the current was increased), arises from the
fact that whereas the magnetic force exerted on a mag-
netic pole at a particular point by a current flowing round
a coil of wire is directly proportional to the current, the
force exerted on the same magnetic pole by the iron core
of an electro-magnet round which the current is flowing
increases nearly proportionately to the current when the
current is small, but becomes nearly constant for all
values of the current above a certain value, in conse-
quence of the magnetic saturation of the iron core. Hence,
by using the force due to a coil without an iron core
for the deflecting force, and the force due to the iron
core of the electro-magnet for the controlling force,
Messrs. Crompton and Kapp have made extremely in-
genious current and P. D. meters, which require the
employment of neither permanent magnets, springs, nor
weights.
The coil of the electro-magnet has a magnetic action
as well as its iron core, and as the former increases in
direct proportion to the current, its action must be neu-
tralised if we wish the controlling force to be constant.
This can be done either by the use of a third coil of a
suitable size and number of convolutions, placed in
such a position that when the current flowing round
the electro-magnet also flows round this coil, its action
exactly neutralises that of the electro-magnet coil, or the
neutralisation may be more simply effected by placing the
deflecting coil in such a position that it is equivalent to
two coils, one the deflecting coil, and the other a coil
whose effect neutralises that of the coil round the electro-
magnet.
205. Paterson and Cooper's Electro - magnetic
Control Meters. — ^These are the same in principle as those
invented by Messrs. Crompton and Kapp, with the addi-
tion of movable pole-pieces similar to those shown in
394 PRACTICAL ELECTRICITY. [Chap. VIII.
Fig. 25, page 74, for adjusting the sensibility of the in-
strument.
The advantage of electro-magnetic control meters is
that, as neither permanent magnets nor springs are em-
ployed in their construction, their sensibility cannot be
affected by variations in their strength, and hence their
behaviour from year to year remains exactly the same.
The disadvantage arises from the fact that as the
entire controlling force, corresponding with that produced
by the powerful permanent magnet in the apparatus
shown in Fig. 23, page 70, for example, has to be produced
by an iron core of the electro-magnet, the mass of iron
must not be too small, otherwise any external piece of
iron or magnet will affect the indications of the instru-
ment. But it is found by experiment that unless the
iron be not only very soft, but also he very small in mass^
there is considerable residual magnetism^ which causes the
magnetic force exerted by the iron to depend not merely on
the strength of the current passing round it at any par-
ticular time, but also on the strength of the previous cur-
rents, and this is. the case even when the iron is still too
small to prevent very serious variations in the reading
of the instruments being produced by the presence of a
neighbouring magnet {see § 210, page 407). The read-
ings, therefore, in the lower part of the scale, instead of
corresponding with definite values of the current, or of
the P. D., correspond with currents or P. Ds. differing in
some of these electro-magnetic control instruments by as
much as thirty per cent., depending on whether it is an
increasing current or a decreasing current that is being
measured. {See § 208, page 402.)
206. Testing Ammeters. — The faults to be looked for
in an ammeter, and for which it must be carefully tested,
are : —
1. An error arising from the ampere-standards em-
ployed by different makers differing from one another.
2. All error arising from a current producing a
Chap. VIII.l CALIBRATING AMMETERS. 395
different deflection, depending on whether the previous
currents passing through the instrument were much
smaller or much larger than the current being measured.
3. An error arising from the instrument indicating a
different number of amperes for the same current when it
is reversed in direction.
4. An error arising from the sensibility of the instru-
ment being temporarily varied bj external magnetic dis-
turbance.
5. An eiTor arising from a permanent alteration of
sensibility, due, for example, to the demagnetisation of a
steel magnet.
207. Test for Accuracy of the Graduation. — It has
been explained in § 6, page 11, that the standard ampere
is that which deposits 0*00111815 grammes of silver per
second. Makers of commercial instruments, however, do
not calibrate each ammeter by comparing it with a silver
voltameter, but only compare it with some standard
current meter which has at some previous time been com-
pared with a silver voltameter, but which may have
changed its sensibility in the interval. To check tlie
accuracy of any ammeter, therefore, it is desirable to com-
pare it directly with a silver voltameter, and in Fig. 157
the apparatus is shown arranged for calibrating a magni-
fying spring ammeter A, in this way. d is a platinum
dish, containing a 25 per cent, solution of silver nitrate,
into which is placed a thick silver disc P, wrapped in filter-
ing paper, to prevent particles of oxide of silver which may
become detached from the silver plate dropping on to the
platinum, and making the weight appear to.be too great.
It is better to use a platinum dish than a silver one, be-
cause the silver deposited at the bottom of the platinum
dish can be removed, and re-formed into silver nitrate by
pouring a little nitric acid into the dish. This could not
be done with a silver dish, as the nitric acid would prob-
ably burn holes in it ; hence the silver dish would gradu-
ally grow thicker and heavier. The platinum dish should
be made as thin and as light as possible, so that it may be
396
PRACTICAL ELECTRICITY.
[Chap. VIII.
accurately weighed ; with a diameter of 4 inches, and a
depth of rather more than 1 J inches, it need not weigh
more than 78 grammes.
This silver disc is held in position by a strip s, at-
tached to it, held in a clamp c, the two sides of which
are pressed together by turning the nut N. The disc
and the strip s are in one piece, cut out of a thicks
Fig. 157.
flat sheet of silver, the strip being bent up at right angles
to the disc after it is cut out.
Electric connection is made with the platinum dish d,
by its resting on three metal pins ^9, connected with the
wire Wg, and connection is made with the silver disc by the
wire soldered to C, the other end of which is connected
with one terminal of the ammeter. The other terminal
of the ammeter is connected through an adjustable carbon
resistance r with the wire w^, and the circuit is closed
by putting the metallic bridge-piece b into the small
mercury cups h h. The current produced by a current
Chap. VIII.]
CALIBRATING AMMETERS.
397
generator, the terminals of which are attached to the
wires w^ and Wg, can be conveniently varied within wide
limits by screwing or unscrewing the nut at the top of
R, shown at n (Fig. 158), separated from the rest of the
apparatus. Screwing this nut n, presses down more or
Pig. 158.
less a wooden washer e, which, in its turn, compresses
more or less a pile of discs of carbonised cloth, some of
which, c^c^ c, c, are seen, in Fig. 158, separated from the
carbon resistance. This cloth is specially prepared by Mr.
Varley, by heating ordinary cloth to an extremely high
temperature in a vacuum, which carbonises the cloth
without destroying its flexibility and elasticity. The
carbon discs are piled up in a heap by slipping them over
a thin wooden tube which surrounds the brass rod 7i, ter-
minated at the top in a screw thread for the nut n to
screw on, and contact is made with the discs by one or
other of three plates of brass, pi, po, p^, one of which,
Pi, is seen separated in Fig. 158, These plates of brass
398 PRACTICAL ELECTRICITY. [Chap. VIIL
are of about the same size as the carbon discs, and the
hole in the centre of each is shaped like the section of
the rod h — that is, not quite round, so that p^ and jOg
can slide up and down this rod without being able to
turn round it.
Starting with a pressure sufficiently great to keep the
discs fairly well in contact, so that they cannot shake
about and thus produce a varying resistance, and gra-
dually increasing this pressure, but not to such an
extent as to damage the discs, the resistance of the whole
column can be varied from about J to 9| ohms when the
discs are about IJ inch in diameter, and when the
height of the column of them is about 3 inches. A re-
sistance still less can be obtained by attaching the wires
to the plates ^^g and/>3 (Fig. 158), instead of to the top
and bottom plates as in Fig. 157.
When adjusting the carbon resistance R so as to
obtain the desired current, it is desirable that no decom-
position should take place in the silver voltameter, for
in that case the drying and weighing of the platinum
dish D would have to be carried out after the carbon re-
sistance was adjusted, and it would probably be found
that a fresh adjustment was required when it was desired
to start the decomposition. To avoid this difficulty, the
circuit through the silver voltameter should not be closed
during the adjustment, but Wg and the left-hand terminal
of the ammeter should be joined instead by a piece of
German silver wire, having the same resistance as the
voltameter. A third mercury cup, not shown in the
figure, but which we may call h', may be easily arranged
so that when the bridge-piece b is put into the holes h and
h', the circuit through the German silver wire is closed,
whereas when one of its ends is shifted from h' to h,
the other being left in the other hole h, the circuit
through the voltameter is closed.
At the commencement of the experiment the platiimm
dish D (Fig. 157) should be carefully washed with distilled
water, to remove any dust or dirt, then dried over a
Chap.VIII.; CALIBRATING AMMETERS. 399
spirit lamp, and placed on the triangle T over the vessel
V of strong sulphuric acid, and the glass cover G left
over while the platinum dish is cooling. When it is
cool it should be carefully weighed. The dish is now
put in position on the pins p, the silver di^jc placed so
that its edges are equally distant from the sides and
bottom of the dish, and the solution of silver nitrate
poured in. Next, a current is sent through the
carbon resistance R, the ammeter A, and the German
silver wire above referred to, and the carbon resistance
adjusted until the current, as observed on the ammeter,
has the right value. The maximum value that may be
given to the current so as to obtain a good adherent
deposit with a particular platinum dish is (as stated in
the foot-note, § 6, page 11) one ampere per six square
inches of surface. At a time noted on a watch
the current is sent through the voltameter instead of
through the German silver wire, and its strength is kept
constant by slightly turning from time to time the nut n
(Fig. 158) at the top of the carbon resistance so as to keep
the ammeter deflection constant, and at a noted time, at
the end of from ten to thirty minutes, depending on the
current used, the circuit is interrupted. The silver
nitrate solution having been put back into the bottle,
the platinum dish, with the layer of deposited silver in
it, is carefully rinsed out with distilled water ; next it is
filled with distilled water, and left standing for ten or
fifteen minutes to remove traces of the silver nitrate
solution, then having been rinsed out again with distilled
water, it is rinsed out with alcohol to remove the water,
and with ether (which evaporates with great rapidity) to
remove the alcohol, and finally it is dried over a spirit
lamp, and left to cool under the desiccator g, when it is
again carefully weighed. Then, if W be the increase in
weight in grammes produced in t seconds by a current of
mean strength, A amperes,
A = ^^— .
000111815 <
400 PRACTICAL ELECTRICITY. (Chap. VIIL
It is desirable to repeat this test for two or three
very different currents that the ammeter is adapted to
measure, as the calibration may be right in even two
very different parts of the scale, and not at some inter-
mediate part, arising from the law of the instrument not
being exactly what the maker has supposed ; for ex-
ample, he may have determined accurately the currents
corresponding with two points of the scale, and have
interpolated the intermediate graduations on the assump-
tion that the increase of deflection was directly propor-
tional to increase of current, which may not be quite
true with the particular instrument.
208. Test for Residual Magnetism. — In order to
ascertain whether a current produces the same defiection
on an ammeter, independently of whether the currents
previously passing through the instrument were much
smaller or much larger than the particular current in
question, the instrument should be joined up in series
with a Siemens' dynamometer, or other current meter
containing absolutely no iron or steel, and, therefore,
having no error due to residual magnetism, together with
an adjustable carbon resistance, care being taken to put
the dynamometer so far away from the other instrument
that any magnetism produced in the latter will not affect
the dynamometer. Then, starting with the carbon re-
sistance unscrewed, so that its resistance is great, the
circuit should be closed, and successive simultaneous
readings of the two instruments taken; first, as the
carbon resistance is gradually screwed down, and the
current increased up to the maximum current the
instrument is intended to measure ; then, as the carbon
resistance is gradually unscrewed, and the current di-
minished again.
The following are the results of such tests made with a strongly
magnetised permanent magnet ammeter, like that shown in Fig.
26 page 76 ; with a spring control meter, like that shown in Fig.
154, page 384 ; with a magnifying spring ammeter, like that
shown in Fig. 156, page 388 ; and with an electro-magnetic control
meter.
Chap.VIII.J TEST FOR RESIDUAL MAGNETISM. 401
Amperes as measured by a Per- Amnereq as mPasnred bv a
6-1 > 6-58
12-2 § • 12-31
18-3 t 18-32
About 24-4 1" Not read
18-3 0 18-3
12-2 § 12-3
6-1 g 6-4
Amperes as measured by a Spring
Control Meter, with, massive iron •a,v,«^^^c „ ^^„„ ^^ u
needle, ajad deflecting electro- ^.^irf,f=^^r»"^^t^l^.?J/
magnets with massive cores; Siemens Dynamometer,
reading from 0 to 100 amperes.
20 ^ 19-6
25 § 25-3
36 g 36-2
45 §' 47-1
65 I' 68-1
58-6 61-4
65 y 57-4
45 I 46-0
35 § 34-4
25 I 23-2
20 cp 17-2
That it requiied a smaller current at the end of the experiment
to produce the same deflection as was produced at the beginning,
showed that the iron core of the deflecting electro-magnet retained
some of the magnetism put into it when the strong current was
flowing round it.
Amperes as measured by the
Magnifying Spring Amme- Amperes as measured by a
ter ; reading from 4*5 to Siemens' Dynamometer.
25 amperes.
5 |> 4-95
10 § 9-9
15 I 15
20 I 20-4
23 "y 24-45
20 g ' 20-85
16 I 15
10 I 9-87
5 ^ 4-86
__ _ _
Lmperes as measured by
the Electro-Magnetic Con-
trol Meter ; reading from 0
to 100 amperes.
10
25
30
1
40
50
(jj
60
60
y
50
m
40
§
30
20
CfJ
10
4:02 PRACTICAL ELECTRICITY. [Chap. VIII.
Amperes as measured by a
Siemens' Dynamometer.
8-82
27-6
32
41-9
52-3
63-5
64-4
53-6
44-3
34-7
24-9
11-5
That it required a much higher current at the end of the
experiment to produce the same deflection as was produced at the
beginning, showed that the iron core of the controlling electro-
magnet retained some of the magnetism put into it when the
strong current was flowing round it.
209. Test for Error on Reversing the Current. —
Certain instruments, such as the spring instrument of
Mr. Cunynghame, and the electro-magnetic control instru-
ments of Messrs. Crompton and Kapp, are intended to be
used only when the current flows through them in one
direction, and therefore they ought not to be inten-
tionally used with the current flowing through them in
the wrong direction. As, however, in the charging and
discharging of accumulators, &c., the current is liable to
be reversed, it is desirable to try experimentally the kind
of error that would be produced if the current were re-
versed, and then reversed back again so as to again flow
through the instrument in the proper direction. To
make the experiment, the instrument to be tested
should be joined in a series with some standard instru-
ment, like a Siemens' dynamometer, and the direction
of the current through the former instrument only
should be reversed, to avoid the possibility of any error
being introduced into the readings by the reversal of
the current through the latter. The two instruments
Chap. VIII.] ERROR ON REVERSING THE CURRENT.
403
must, of course, be placed so far apart that tlie reversal
of the magnetic action of the one, when the current
passing through it is reversed, does not affect the other
directly.
With instruments having much iron, it is found that
not merely are the readings which are obtained with the
same current when flowing in different directions very
different, but that even when the current has been twice
reversed, so as to flow again in its original direction, the
value of a small current, as determined from the indication
of the instrument, is very different from its true value,
and this is especially the case when a strong current
was used in the first reversal, and only a weak one in
the second.
Amperes as measured by a Spring Control Meter,
Amperes as mea-
with massive soft iron needle and deflecting
sured by a Sie-
electro-magnet with massive cores; reading
mens* Dyna-
from 0 to 100 amperes.
mometer.
At first 21.
20-8
A reverse current of 100 amperes was now
sent through the instrument for 30 seconds,
then the original current in the original
direction, the deflection now was
18-8.
20-8
A reverse current of 85 amperes was next
sent for 30 seconds, next the original current
in the original direction, the deflection was
still
18-8.
20-8
A direct current of 100 amperes was sent
for 30 seconds, and then the original current
the deflection now became
19-75,
20-8
and slowlv increased to
20.
20-8
210. Test for Error Produced by External Magnetic
Disturbance. — To test this a steady current should be
404 PRACTICAL ELECTRICITY. fCliap. VIII.
sent through the instruments, and the readings taken
first with no outside magnet near, then, when a fairly
strong bar magnet is moved round in a plane passing
through the centre of the instrument, the magnet being
held so as to always point towards the centre of the in-
strument, and with its end at always the same distance
I
Morixonial Plc^ne
\
Fig, 159.
from the centre. A foot is found to be a convenient
distance to take, and the plane in which the bar magnet
is moved should be that in which the magnet must pro-
duce the greatest disturbance ; for example, with an in-
strument having a needle turning round on a vertical
axis, the plane in which the magnet is moved should
be horizontal^ as shown in Fig. 159, whereas with a
magnifying spring instrument in which the soft iron tube
Chap. VIII.] TEST FOR EXTERNAL MAGNETIC DISTURBANCE. 405
TT (Fig. 156) is pulled downwards, the plane should be
a vertical one, as seen in Fig. 160.
The experiment should be made with a weak current
passing through the instrument, and also with a strong
one, as frequently the magnetic disturbance differs in
d
Vertical PUitie
I
Fig. 160.
amount for different currents, and in both cases the con-
stancy of the current during the experiment should be
assured by its passing also through some other instru-
ment, such as a Siemens' dynamometer, placed so far
away that the motion of the magnet does not affect it.
406
PRACTICAL ELECTRICITY.
LCkap. VIII.
The following show the results of this test made with several
instruments, always using the same permanent magnet to produce
the disturhance at the same distance from the centre of the instru-
ment.
Magnet moved round a Fermanent Magnet Ammeter in a Horizontal
Plane.
Amperes aa mea-
sured by the Per-
manent Magnet
Ammeter ; read-
ing from 0 to 25
amperes.
22-2
22-1
22-4
22-3
220
22-2
Amperes a
measured by
a Siemens' Dy-
namometer,
22-0
220
22-0
22-0
22-0
22-0
No magnet near.
Magnet in position a
No magnet near.
Fig. 159.
Magnet moved round a Magnifying Spring Ammeter in a Vertical
Plane.
Amperes as mea-
sured by the Mag-
nifying Spring Am-
meter ; reading
from 4-5 to 25 am-
Amperes as
measured by a
Siemens' Dy-
namometer.
peres.
6
6
6
6
6
6
5-59
6-59
5-59
5-59
5-59
5-59
No magnet near.
Magnet in position a
No magnet near.
Fig.
160.
21
21
21
21
21-5
21-5
21-5
21-5
No magnet near.
Magnet in position a
»» » *
^Fig.
160.
21
21-5
f> >» ^
)
21
21-5
No magnet near.
Chap.Vni.l TEST FOR EXTERNAL MAGNETIC DISTURBANCE. 407
Magnet moved round an ElectrO'tnagnetic Control Meter
Hcrlzontal Plane.
Amperes as measured
by the Electro-mag-
Amperes as measured
netic Control Meter ;
by a
Siemens'
Dy.
reading from 0 to 100
namometer.
amperes.
10
9-2
No magnet near.
10-1
9-2
Magnet in position a.
14-6
9-2
5> » *•
10-9
9-2
>) J> ^»
7-9
9-2
« » ^'
9-5
9-2
No magnet near.
82
90
No magnet near.
81-8
90
Magnet in position a.
84-6
90
84-6
90
» » ^'
81-3
90
» » ^'
82-2
90
No magnet near.
211. Test for Permanent Alteration of Sensibility.—
This test is one that must necessarily extend over a long
period, as permanent magnets are found to slowly de-
magnetise, springs to become permanently strained, or,
as it is called, get a ^^ permanent set" &c. Frequent com-
parisons should, therefore, be made between the readings
of an ammeter, and the amount of silver deposited in a
given time by the currents giving these readings.
Errors in Voltmeters.
212. Testing Voltmeters. — In addition to the five
errors given in § 206, page 394, and which affect volt-
meters equally with ammeters, there is a most important
sixth error arising from the sensibility of a voltmeter
varying with its resistance, and, therefore, with its tem-
perature. This change of resistance is due partly to the
variation of the temperature of the room, and partly to
the coils of the instrument becoming heated by the
408 PRACTICAL ELECTRICITY. LCbap. VIIL
passage of the current through them. Voltmeters in this
respect differ entirely from ammeters; an increase of
resistance of an ammeter may diminish the current in
the circuit, but the ammeter will accurately measure the
current so diminished ; consequently, the sensibility of an
ammeter is unchanged by a change in the resistance alone.
For example, if two exactly similar ammeters be wound,
the one with copper, and the other with German silver
wire of the same gauge, and with the same number of
convolutions, the sensibility of the one will be exactly
the same as that of the other, in spite of the resistance
of the latter instrument being thirteen times that of the
former; whereas an increase in the resistance of a
voltmeter causes a less current to pass through it for the
same P. D. at its terminals, and hence the sensibility
of a voltmeter varies with change in its resistance.
213. Test for Accuracy of the Graduation. —
From the definition of a volt (§ 81, page 141), it follows
that if we know the current in amperes passing through
a resistance, the value of which is known in ohms, we
know the P. D., in volts, at its terminals, since this is
equal to the product of the number of amperes into the
number of ohms. This leads to a very simple and accu-
rate method for calibrating voltmeters, and which is
shown symbolically in Fig. 161. v is the voltmeter to
be calibrated, r^ a resistance formed of a long coil of
fairly thick copper, or better of platinoid wire wound
double so as not to produce any external magnetic
action, and coiled up loosely so as to cool fairly quickly.
A is an ammeter which has been accurately graduated,
and w a Wheatstone's bridge, or differential galvanometer,
with battery complete for measuring the parallel resist-
ance between the points c and b, and which is made up
of r^ and of v. Between the terminals t^ and Tg, there is
some suitable current generator, not shown in the figure,
which will send a current through the arrangement
on inserting the plug p^ ; rg is an adjustable, but not
necessarily a known, resistance for varying this current,
Chap. VIII. ] CALIBRATING VOLTMETERS. 409
and Pg is a plug key for completing or interrupting the
circuit through the measuring apparatus w.
The experiment is performed thus : — Pg being opened
and p^ closed, re, is adjusted so that a convenient deflec-
tion is obtained on v. This deflection is read by one
observer, and simultaneously the deflection on a by
another observer, when, on a signal being given at which
the time is noted, p^ is opened, Pg is closed, and time mea-
surements of the parallel resistance between c and b
taken. These resistances being plotted as ordinates on
Fig. 161.
a .sheet of squared paper with the times, from the moment
of opening p,, as abscissae, a curve can be drawn, and on
producing it backwards it is easy to ascertain what was
the exact resistance in ohms and fraction of an ohm of
the circuit between c and b at the moment the simul-
taneous readings on v and A were taken, then the product
of this resistance into the number of amperes gives the
exact number of volts corresponding with the deflection
on V. rg is now varied so as to produce a diflferent deflec-
tion on the voltmeter v, and the number of volts corre-
sponding with it ascertained as before, and so on for
as many readings as it is necessary to take to determine
the absolute calibration of the voltmeter.
If the coil r^ be made of very thin German silver
wire, and the current sent through it be only a small
J^rU. ^A3c(ic^ £<^c4.
410
PRACTICAL ELECTRICITY.
CChap. VIII.
one, the resistance may not alter by the passage of the
current; but if it be desired to produce a P. D. of
100 or more volts between the points c and b, and to
use an ordinary ammeter a, graduated up to, say, 20
amperes, the resistance 7\ would have to be something
like 10 ohms, and able to take a current of 10 amperes
without heating at all. Such a wire would have
to be very long and thick, and, therefore, expensive,
whereas the device of taking time measurements of the
resistance enables the coil to be made of even copper
wire.
The preceding method is based on our knowing the
exact value of a current and of a resistance, but we may
calibrate a voltmeter by comparing its readings with the
E. M. F. of a cell, if this E. M. F. be accurately known
in volts. The cells best suited for this purpose are a
^^ Latimer Clark's cell" or
some form of gravity
Daniell, in which the cop-
per sulphate and zinc sul-
phate solutions mix very
slowly.
214. Latimer Clark's
Cell. — These cells are made
in a variety of forms, "^ but
probably what is called the
H form, shown in Fig. 162,
is the best. One of the
legs is partially filled with
an " amalgam of zinc " A,
formed by putting some
pure zinc into pure mer-
cury, which has been previ-
ously distilled in a vacuum^
the other with pure mercury m, which has been similarly
distilled, covered with a layer of ^'mercurous sulphate'^ m s.
* Phil. Trans. Koy. Soc, vol. xvii., p. 411. Part II., 1884.
Fig. 162.
Chap-VniJ LATIMER CLARK'S CELL. 411
The whole is then filled up above the level of the cross tube
with pure saturated zinc sulphate z, and a few crystals of
zinc sulphate are added. Evaporation is prevented by the
insertion of paraffined corks C, and electrical contact is
made with the amalgam, and with the pure mercury, by
platinum wires w w, sealed into the glass. Marine glue
may be employed instead of paraffin wax to make the corks
C air-tight, or, best of all, the upper ends of the tubes
may be hermetically sealed {see note, page 20). If the
zinc sulphate be saturated, h\\.t not ^^super-saturated"*
the experiments of Lord Rayleigh t show that when
this cell is not allowed to send currents, its E. M. F., after
it has been set up for some weeks, is extremely constant
for the same temperature, and has a very exact value
for any particular temperature ; its value in legal volts
being equal to
. 1-438 {1-0-00077 («- 15°)},
where t is the temperature of the cell in degrees Centi-
grade.
As in the DanieH's cell {see § 119, page 211), a
diminution in the density of the zinc sulphate solution
increases the E. M. F. of the Latimer Clark's cell.
215. Standard Daniell's Cell. — In spite of the great
value of the Latimer Clark's cell, it has two defects, the
one that it polarises rapidly, and its E. M. F. temporarily
falls off if a current be allowed to pass through the cell,
the other that the variation of its E. M. F. with tempera-
ture is considerable, and therefore for accurate work the
temperature of the cell must be accurately known. These
* When a saturated solution of a salt is cooled, some crystals are
formed so as to leave the liquid simply saturated at the lower tem-
perature ; but if the liquid be closed up so that the air does not get to
it, and if it be cooled without shaking, crystallisation may not take
place, and the liquid is thensaidjto be " super-saturated," for on dropping
a crystal of the salt into it, crystallisation immediately occurs. The
presence, therefore, of crystals in a liquid is a proof that it is satu-
rated and not super-saturated.
t Proc. Roy. Soc, vol. xl., p. 79.
412
PRACTICAL ELECTRICITY.
[Chap. VIII.
objections are overcome by the employment of a form of
gravity Daniell, in which the solutions can only mix
very slowly. If the plates, or rods, be formed of clean,
pure zinc, and of freshly " electrotyped " copper — that is,
copper on the surface of which a layer of copper has
been deposited by putting
the plate, or rod, into a
bath of copper sulphate,
and sending a current
through the bath, so that
it leaves by the plate or
rod — and if the solutions
used in the DanielFs cell
be formed of pure crystals
of copper sulphate and
zinc sulphate, then the
E.M.F. will be 1-104 volts
when the solutions are
equally dense, and 1*074
volts if the copper sulphate
solution has a specific
gravity of MOO at 15° C,
and the zinc sulphate solu-
tion 1'400 at the same
temperature. A form of
gravity Daniell's cell, spe-
cially designed by Dr.
Fleming,* to be used as a
standard, is shown in Fig.
163, and consists of a U-
tube j inch in diameter,
and 8 inches long, provided
with glass taps, &c., as shown. To use the cell, the tap
A is opened, and the whole XJ-tube filled with the denser
zinc sulphate solution ; the zinc rod which is kept in the
test tube l, when the cell is not in use, is now inserted in
the left-hand tube, and its indiarubber stopper p fitted
* Phil. Mag., S. 5, vol. xx., p. 126.
Fig. 163.
Chap.VIII.l- STANDARD DANIELL's CELL. 413
tightly into this tube. Now, on opening the tap c, the
level of the liquid will begin to fall in the right-hand
limb, but no liquid will flow out of the left-hand one.
As the level commences to sink in the riglit-hand limb,
copper sulphate solution can be allowed to flow in gently
to replace it by opening the tap b ; and this opera-
tion can be so conducted that the surface of demarcation
of the two liquids remains quite sharp, and gradually
sinks to the level of the tap c. When this is the case,
all the taps are closed and the copper rod is removed from
the test tube m, in which it is kept, and, after having been
freshly electrotyped, is fitted into the right-hand tube Q.
It is impossible to stop the liquids mixing together
at the surface of contact, but whenever the surface of
contact ceases to be sharply defined, the mixed liquid at
the level of the tap c can be drawn off, and fresh solu-
tions supplied from the reservoirs above.
Experiment shows that the effect of oxidation of
the zinc is to lower the E. M. F., while oxidation of the
copper raises it.
In order that the E. M. F. of a Latimer Clark's cell
should be quite constant, it is absolutely necessary that
the cell should not be allowed to send any appreciable
current, and even with the Daniell's cell better results
will be obtained if the cell be not sending a current when
the test is made, since in that case the P. D. at its
terminals will be equal to the E. M. F., independently of
the internal resistance of the cell, which will be rather
high if it be so constructed that the solutions can only
mix slowly. Hence, Poggendorff's method (see § 132,
page 234), or the condenser method (see § 183, page 341),
must be employed, care being taken to determine accu-
rately the multiplying power for a discharge of the shunt
employed (see § 188, page 349).
The complete arrangement for calibrating a voltmeter
by Poggendorff's method is shown in Fig. 164, the
figure being somewhat distorted so that the details of
the key can be easily seen. In actual practice the
414
PRACTICAL ELECTRICITY.
[Cliap. VIII.
board and the wires on it are much longer than they
appear to be in the figure. J K is a long German
silver, or platinum-silver, or platinoid wire, very care-
fully drawn so as to have, as nearly as possible, the
same diameter everywhere, and as it is very difficult, if
not impossible, to draw a long wire having exactly the
same diameter at all points in its length, the resistance
of each five or six inches of the wire should be carefully
Fig. 164.
measured and recorded, b is a large battery of any kind
of cells that will send through r^, and the wire J k, a
current that will remain constant for at any rate a few
seconds. G is a sensitive high resistance galvanometer,
s the standard cell, and r^ is a high resistance inserted in
this circuit to keep the current that would flow through
the cell on closing the key quite a weak one, eveii if
the point of contact of the key with the wire J K be far
away from the position that gives no current through the
galvanometer. The test is made by inserting the plug p,
the handle H of the key being up, and adjusting 7\ until
the P. D. between the points J and K, that is, between
Chap. VIII.] CALIBRATING VOLTMETERS. 416
the terminals of the voltmeter v, produces about the
desired deflection ; the key is then closed for a moment,
when, if there be any deflection on G, the key is slid, in
the proper direction, along the wire J K, and contact
again made, and so on until a point m is found such that
no current passes through g ; the reading on v is taken
at that moment, and we know that it corresponds with a
P. D. equal to
resistance ofjK ^ ^^ ^ „ , ,,,,
— : X E. M. F. of the standard cell.
resistance of jm
In order to enable the contact-maker c to touch any one
of the five wires composing J k, c can be slid along the
slot in the lever ; and, to prevent the platinised knife-
edge attached to the lower part of c being pressed too
hard against the stretched wire, and damaging it, the
flat spring s is made rather weak. Hence, on depressing
H, the knife-edge attached to c first comes into contact
with the wire, and, on still further depressing H until it
comes against the stop placed underneath it, the lever
turns about the knife-edge.
216. Test for Heating Error. — The various errors
found in ammeters occur, as already explained, also in
voltmeters, and may be tested for in the same manner by
using a voltmeter with no iron employed in its construc-
tion, as the instrument of comparison, instead of an
ammeter. As, however, the heating error (see § 212,
page 408) is one peculiar to voltmeters, and may exist
in the voltmeter which we use as our standard when
testing for the other errors, it is desirable to consider
how it may be reduced to a minimum, since the existence
of this heating error in the standard voltmeter might
easily mask all the other errors in the voltmeters that
are being tested. The first point to determine is the
way in which the sensibility of a galvanometer, with
coils of a given shape and size, and with a given needle
and controlling force, varies with the resistance of the
416
PRACTICAL ELECTRICITY.
[Chap. VIIL
wire employed in winding it ; next, how the rate of pro-
duction of heat, when a given deflection is produced, also
varies with the resistance of the wire employed in wind-
ing the galvanometer, because it may be that by winding
it with some special form of wire, we may obtain con-
siderable sensibility with but little heating of the coils.
217. Variation of the Sensibility of a Galvano-
meter with its Resistance. — When all the convolutions
of wire occupy the same position relatively to the needle,
^HR'
c
r't^f/'
Q
Fig. 165.
we nave seen (§^22, page 51) that the sensibility of a
galvanometer is directly proportional to the number of
convolutions — that is, to the length of wire employed in
winding the bobbin. This conclusion is also true, no
matter what be the shape of the coil, or what the
distances of the various convolutions from the needle,
provided, that the coil is Jixed in size and shape ; for
let A B c D, a' b' c' d ' (Fig. 165), be a small bit of a sec-
tion of a galvanometer coil taken through the axis p Q
of the coil ; A B c t) being so small that all the three
wires that pass through it are at practically the same
distance from the needle, and therefore produce the
Chap. VIII.] GALVANOMETER SENSIBILITY AND RESISTANCE. 417
same magnetic effect when the same current passes through
each of them. Now, if the bobbin were wound with
wire of half the diameter, there would be four wires for
each of the three wires that pass through abcd, or
twelve altogether, as in Fig. 166, hence the magnetic effect
due to the wires that pass through the small bit a b c d,
a' b' c' d' would, for the same current, have been increased
four times. And so for the wii'es passing through any
other bit r s t u, r' s' t' u' of the section. Hence, although
the magnetic effect of one convolution passing through
abcd, a' b' c' d' may, for the same current, be very
different from the effect of a convolution passing through
R s T u, r' s' t' u', we may say that the lohole magnetic
effect for the same current is directly proportional to
the number of convolutions, or to the length of the wire ;
and it will be observed that this result remains true even
if the diameter of the wire at different parts of the coil
be quite different, provided that the law of winding be
maintained when the gauge is changed — that is to say,
the diameter of the wire used in winding the three con-
volutions passing through abcd may be quite different
B B
418 PRACTICAL ELECTRICITY. [Cliap. VIIL
from that employed in winding the three convolu-
tions passing through r s t u, and yet the whole magnetic
effect for the same current will be directly proportional
to the length of the wire, provided that when we halve,
double, or treble the diameter of one set of wires, we do
the same for every other. We may conclude, therefore,
that when we have a galvanometer with coils of a
given shape and size, wound according to a given law,
and fitted with a given needle, or set of needles,
and controlled by a given force, the sensibility of the
galvanometer is directly proportional to the number of
convolutions^ or to the length of wire used in wind-
ing it.
But the resistance of the wire used in winding a
given coil is, for the same material, copper, German
silver, &c., proportional to the square of the number of
convolutions — that is, to the square of the length — be-
cause when we replace each convolution by four, we
make the length of the wire used in winding the bit
A B c D, a' b' c' d' four times as great, and the sectional
area of each wire one-quarter, therefore the resistance of
the wire passing through A B c D, a' b' c' d' becomes six-
teen times as great, and so for the wire used in winding
any other small bit R s T u, r' s' t' u', hence the sensibility
of a galvanometer is directly proportional to the square
root of its resistance, and the rnagnetic effect is directly
proportional to the product of the current into the square
root of the resistance.
Therefore, with coils of a given shape and size,
wound according to a given law, with wire of a given
material, and fitted with a given needle, or set of needles,
controlled by a given force, the- current required to pro-
duce a given deflection is inversely proportional to the
square root of the galvayiometer resistance.
And since the current passing through a galvanometer
is equal to the P. D. maintained at its terminals, divided
by its resistance, it follows that the P. D. required to be
maintai7ied at the terminals of a given voltmeter j wound
Chap.Vin.J RATE CURRENT HEATS A GALVANOMETER. 419
with wire of a given material^ to produce a given deflection
is directly proportional to the square root of the resistance
of the voltmeter.
And these two last conclusions may be shown to be
true whether the needle be a hard steel magnet or a
piece of soft iron magnetised by the current passing
round the coils of the instrument.
218. Rate of Production of Heat in Galvanometer
Coils. — We have seen in the last section that the cur-
rent required to produce a given deflection is inversely
proportional to the square root of the galvanometer re-
sistance, and this is the same thing as saying that to pro-
duce a given deflection the product of the current into the
square root of the resistance must be constant. But the
rate of production of heat in the galvanometer is, by § 1 1 3,
page 198, proportional to the product of the square of
the current into the resistance of the galvanometer.
Hence, with coils of a given shape and size, wound ac-
cording to a given law, with wire of a given material,
and fitted with a given needle, or set of needles, controlled
by a given force, the rate of production of heat, when a
given deflection is being produced, is a constant and is in-
dependent of the gauge of wire used in winding the coils.
Hence, we see that iJE the following things be fixed in
a voltmeter : —
1. The shape and size of the coils ;
2. The material of which the wire is made ;
3. The law of winding, i.e., the variation of the
thickness of the wire with the diameter, or position, of a
convolution ;
4. The needles and the controlling force ;
we cannot diminish the error arising from the heat^
ing of the coils when a current passes round them by
winding the instrument with finer or with thicker wire.
We have next to consider whether it may be diminished
by varying 2, 3, or 4. As to 4, it is quite clear that the
smaller the controlling force, and the more astatic the
system of needles (see § 152, page 282), the smaller will
420 PRACTICAL ELECTRICITY. [Chap. VIII.
be the current required to produce a given deflection, and
therefore the less the heating error. As to the material,
if we are merely concerned with variations of resistance
of the voltmeter arising from changes of temperature of
the room, then it is better to use German silver, platinum-
silver, or platinoid wire {see § 94, page 160), or we may
add a small piece of carbon in series with the voltmeter
coils of such a length and size that its diminution of re-
sistance for an increase of the temperature exactly balances
the increase of resistance of the coils ; but if it is the
increase of resistance due to the heating of the coil by
the passage of the current that we wish to have as small
as possible, then it is easy to show that it is better to
wind the whole of the coils with copper wire than with
German silver. For, since the resistance of German
silver for the same length and thickness is about thir-
teen times as great as that of copper, it follows, if two
exactly similar voltmeters be wound, the one with Ger-
man silver wire, and the other with copper wire of the
same length and thickness, that the rate of production of
heat when there is the same deflection in the two instru-
ments (which will be produced by the same current)
will be about thirteen times as great in the one that
is wound with German silver wire, as in the one
that is wound with copper wire, whereas for the same
rise of temperature the increase of resistance of copper
is only about 8*8 times that of German silver {see § 94,
page 160). We cannot, of course, say that the rise of
temperature is proportional to the rate of production of
heat {see §111, page 194), but it is probable that the
rise of temperature of the German silver coils will be
more than 8*8 times that of the copper ones, and, there-
fore, as far as the heating due to the passage of the cur-
rent is concerned, copper is to be preferred to German
silver wire.
The law of winding that will give a minimum heat-
ing error will depend on the dimensions of the instru-
ment, and for a magnifying spring voltmeter of the
Ctap. Vni.] VOLTMETERS WITH SEPARA.TE RESISTANCE. 421
dimensions shown in Fig. 156, and where the radius of
the central part not wound with wire is one-eighth of
the radius of the cylinder formed by the outside of the
wire, it may be shown that, if a be the sectional area of
the copper wire at any distance d from the axis of the
instrument,' and a^ the sectional area of the first layer of
the copper wire nearest the central portion, to have a
minimum heating error the following condition should
be satisfied : —
80 that the sectional area of the outside wire should be
2*395 times the area of the inside wire.
The particular sectional area given to the innermost
wire must depend on the strength of the spring and the
P. D. that it is desired shall produce a particular deflec-
tion.
A method that is frequently employed for diminish-
ing the heating error, is to wind the voltmeter so that a
comparatively small P. D. maintained at its terminals
will produce a large deflection, and then to add a separate
resistance coil joined in series with the voltmeter, when
the practical terminals of the instrument become the free
end of this resistance coil and the free end of the volt-
meter. If Vj be the P. D. in volts required to produce
a deflection of, say, 100° when applied directly to the
terminals of the voltmeter of resistance r^, and Vg be the
P. D. required to produce the same deflection when a
coil of resistance r^ is put in series with the voltmeter,
Hence, by giving a proper value to rj, we can make Vg
have any value we like, but what is even more important,
the temperature error arising from changes of tempera-
ture of the room as well as from the heating of the coils
by the passage of the current round them, will depend
422 PRACTICAL ELECTRICITY. [Chap. VIII.
not merely on the variation of r^, but on the variation of
^1 + ^2> ^^^ tJiis we can keep as small as we like by
making r^ large compared with r^, and by constructing
the extra resistance of thick German silver wire, so that
the proportional increase in the total resistance r^ -f r^
shall be small, even if the increase in r^ alone be con-
siderable. It might be asked, why not make the volt-
meter itself large, and wind it with such thick wire that
the heating would be small. The answer is that if we did
so we should remove the outer layers of wire so far
away from the attracted needle, that the effect of a cur-
rent passing round them would be very small, and hence
we should seriously diminish the sensibility of the in-
strument. The separate resistance coil has to produce no
magnetic action, hence the objection to using very thick
German silver wire in it, and making it very large, is
merely increase in cost and diminution in portability.
There is, however, one objection to making r^ large
compared with r^, and that is, that the energy expended
in the voltmeter itself, and which is equal to 44*25 AVj
footpounds per minute {see § 114, page 201), is only a
small fraction of the energy expended in the extra re-
sistance, and which is equal to 44*25 AVg foot pounds
per minute. The former waste we cannot help, as it is a
constant depending on the construction of the spring and
the shape of the voltmeter (see § 218, page 419), but the
latter is a large waste introduced solely to diminish the
heating error. Hence, a voltmeter, with a powerful con-
trolling force, wound with thick wire of low resistance,
and. furnished with a separate coil of high resistance, can
only he used in electric light, or power, installations where
a small waste of energy is unimportant.
219. Standard Voltmeter. — But if the controlling
force be weak, then the total waste of energy will be so
small as to be negligible, and hence we are led to the
best form to give to a standard voltmeter : suspend the
needle as delicately as possible, and use a controlling
force as weak as is compatible with the instrument
Chap. VIII.] CARDEW'S VOLTMETER. 423
retaining a fixed constant, wind the instrument with not
very fine copper wire, and place in series with it a large
resistance made of as thick platinoid wire as is obtain-
able. When, as explained in § 11, page 23, a galva-
nometer has a single suspended magnetic needle, the
alteration of its strength will not affect the sensibility of
the instrument ; but if there be an astatic combination,
an increase or diminution of strength of either of the
needles will affect the sensibility of the instrument, hence
it is better to use a single needle galvanometer when we
desire gi'eat constancy in the sensibility, as in a standard
voltmeter.
220. Cardew's Voltmeter. — This voltmeter, designed
by Captain Cardew, R.E., differs from all the instruments
previously described in that the heating and not the
magnetic action of a current is employed, and the eleva-
tion of temperature of the conductor is measured by
its expansion. The conductor consists, in the newest
form of the instrument, the back of which is seen in
Fig. 167, of about thirteen feet of platinum - silver
wire 0'0025 inch in diameter. This wire, which is fixed
at one end to a screw A, passes, at the top of the instru-
ment, over a pulley Pj, made of bone so as to be an
insulator, then down under a small bone pulley p^, then
up again over a bone pulley Pg, and lastly is fastened to
a screw b. The pieces of brass into which the screws A
and B are fastened, are connected with the terminals T,
and Tg, and on a P. D. being set up between these ter-
minals a current flows through the stretched wire, the
strength of which depends on the P. D. maintained be-
tween the terminals of the voltmeter, and on the resist-
ance of the wire. The wire becomes hot and expands,
and as it is very thin, it very quickly acquires the
temperature corresponding with the particular current
passing through it. The support carrying the little
pulley j(?i, is pulled down by a thread wrapped round the
grooved wheel w and fastened to the spring s^; hence
when the wire lengthens, and the little pulley p^ descends,
Fig. 167.
Chap. Vin.] CARDEW'S VOLTMETER. 425
the wheel w is turned. The staff (or little shaft) carry-
ing the wheel w also carries a toothed wheel l, geared
into a small pinion M, hence when, by a slight lengthening
of the wire, w is turned through a small angle, the pinion
turns through a large one. On the farther end of the
staff carrying the pinion there is fixed, in the front of
the instrument, a pointer moving over a dial graduated
in volts, the back of which is seen in the figure; con-
sequently the pointer is caused to move right round the
scale by a comparatively small descent of the pulley -p^.
It will be observed that the pull of the spring s^ is
balanced by twice the tension in the stretched wire, and
that the descent of the pulley j>^ is due to the expansion
of only half the total length of wire employed, that is,
the expansion of only about six feet six inches of wire.
The advantage, however, of using a long wire, fixed in
the way shown, instead of a wire half as long, and of
twice the sectional area, which would enable the same
spring Si to be used and cause the same motion of the
pointer for the same elevation of temperature, is that the
fine wire heats and cools much more rapidly than the
thicker one, and so makes the voltmeter much more dead-
beat. If the P. D. to be measured is between 30 and
120 volts, the stretched wire alone may be used, but for
larger P. Ds., an extra resistance {see § 218, page 421) is
added, and the terminals of the voltmeter are now Tj
and T3. If the extra resistance be equal to that of the
voltmeter itself, not merely when the wires are cold, but
also when they are heated by the passage of the current,
the readings on the scale will correspond with exactly
twice the number of volts ; or a double scale somewhat
similar to that seen in Fig. 26, page 76, can be employed,
the numbers on the one being twice the corresponding
ones on the other. To insure the resistance of the
added wire being always exactly equal to that of the
voltmeter itself, Captain Cardew uses for the extra cir-
cuits a stretched wire of the same length and section, and
platted under similar conditions as regards cooling as the
426 PRACTICAL ELECTRICITY. [Chap. VIII.
wire of the voltmeter itself, both sets of •wirts being sur-
rounded with metal tubes, as will be described farther on,
and the tubes, like the metal rods supporting the pulleys
Pi, P2, Pg, P4, being lamp-blacked on the surface. This extra
wire, which has one end attached to the screw c, passes
over a bone pulley P3 at the top of the instrument, then
down and under the little bone pulley p2, then up and
over the bone pulley P4, and lastly is attached to the
spring Sj. The support carrying the pulley p2 is also
attached to a spring S3, hence the stretching of the
second wire which occurs when the current passes
through it is taken up by the contraction of both the
springs 83 and S3, and the wdre is kept tight. To prevent
draughts of air cooling the stretched wires they are en-
closed in metal tubes 1 1, t' t', shown in the figure separated
from the rest of the apparatus. The internal diameter
of these tubes is only a little greater than that of the
circular metal plates, d e, f g, carrying the bearings on
which the pulleys p^, Pg, P3 and P4 turn, so that when the
tubes are slipped over the plates and screwed on to J k,
the top of the box, they prevent these plates having any
lateral motion.
To prevent the rods which support the pulleys p^, Pj,
P5, P4 expanding and contracting more or less than the
stretched wires when the temperature of the room
changes, which would cause the pointer to move, these
rods may be composed partly of brass and partly of iron,
so that their mean co-eflBcient of expansion is the same
as that of platinum-silver.
The mechanism contained in the wooden box in the
lower part of the instrument is protected from damage
by the box being closed with a wooden back (not shown
in the figure) which turns on the hinges H H.
The two great advantages of this instrument are : —
First, it has no heating error, since the elevation of the
temperature produced by the passage of the current is
the property of the current made use of; second, it
can be used for measuring alternating P. Ds. {see § 113,
Chap. VIIL] CARDEW'S VOLTMETER. 427
page 198). As already stated (§ 100, page 174), when a
current is started round an electro-magnet, it takes a
certain time to reach its maximum value, so that with an
alternating current, which is continually being started in
opposite directions, the effecV of the self-induction of the
coil is to practically increase its resistance by an amount
which varies with the rapidity of the alternations ; hence,
apart from the fact that the rapid reversals of magnetism,
which are produced by an alternating current, prevent
an ordinary galvanometer being used for measuring such
a current, even a high resistance dynamometer, which
can be used for measuring an alternating current (see
§ 199, page 381), cannot be used for measuring an
alternating P. D., for its self-induction would cause it
to practically have a variable resistance, and we have
seen (§ 212, page 408) that any variation in the resist-
ance of a voltmeter varies its sensibility. But as the
self-induction of a straight wire bent back on itself is
very small, the error in Captain Cardew's voltmeter,
arising from self-induction, is negligible, and so this in-
strument is much used for measuring an alternating
P. D. It is also dead-beat, direct-reading, not disturbed
by magnets, and fairly portable, although large.
The disadvantages of the instrument, as usually made,
are : — First, it absorbs a good deal of energy ; second, it
cannot be used for measuring a small P. D., for we can-
not make it of thicker wire as we should do in the case
of an ordinary voltmeter intended to measure small
P. Ds., as this would render it sluggish, since a thick
wire traversed by a current heats and cools slowly on
starting and stopping the current; third, there is con-
siderable vagueness in the readings near the zero point,
and sometimes inaccuracy in the upper parts of the scale.
221. Commutator Ammeter and Voltmeter. — With
any of the magnetic instruments already described, the
following com mutating device, due to the author, may be
employed, and which enables the same instrument to be
used with two degrees of sensibility, the one exactly a
428
PRACTICAL ELECTRICITY.
[Chap. Vni.
certain known number of times the other. This arrange-
ment is very convenient when an ammeter has at one
time to be nsed to accurately measure, say, the current
passing through an arc-lamp, which may be 20 or more
amperes, and at another time to measure with equal
accuracy that passing through an incandescent lamp,
which will most probably be less than one ampere, or
when the same voltmeter is to be employed to measure
Fig. 168.
the P. D. at the terminals of a dynamo machine, and
which may be 100 or more volts, and the P. D. at the
terminals of five or six cells. Further, this power of
varying the sensibility in a known ratio is of especial con-
venience in enabling an ammeter which is to be employed
for measuring strong currents, or a voltmeter that is used
for measuring large P. Ds., to be accurately calibrated
by using, in the one case, known currents, and in the
other known P. Ds. only one-tenth as large as the instru-
ment can be employed to measure. The device consists
in winding the instrument with a strand of separate
Chap. VIII.] COMMUTATOR AMMETER AND VOLTMETER. 429
wires instead of merely one wire, and employing a
" commviator,^^ by means of which the current can be
made to go either through all the wires in parallel, as if
through a single thick wire, or, instead, through the wires
one after the other in series, as if the instrument were
wound with one long fine wire. Such a commutator is
seen under a cover at the back of the ammeter shown in
Fig. 26, page 76, and the commutator with the cover
Fig. 169.
removed is shown in Fig. 168, part of the side and some
of the springs being removed to show the remainder more
clearly. One end of each of the wires is permanently
attached to the upright springs So, Sg, s^ &c. (Fig. 169),
on one side of the ebonite barrel of the commutator
cc, and the other end of each of the wires to one of
the upright springs s'g, s'g, s\, &c., on the other side
of the barrel. In one of the positions of the commu-
tator, all the springs on one side are electrically con-
nected together by a platinised strip of brass bb, in-
serted in the barrel of the commutator parallel to its
axis of rotation, and all the springs on the farther side
430
PRACTICAL ELECTRICITY.
[Chap. VIII.
are also connected by a similar piece of metal b' b',
inserted in the other side of the ebonite barrel, the
tips of the springs being also platinised to insure
good contact. The terminals marked p, p s, seen at the
back of Fig. 26, are permanently connected, by pieces of
thick wii'e in the base of the instrument, to the first of
each of the springs Sj, s\, on the two sides of the barrel,
hence the connections are now as shown symbolically
Fig. 170.
in Fig. 169. If, however, the barrel of the commutator
be turned through a right angle, the metal bars b b, b' b'
are removed from the position in which they touch the
springs, and, instead, pins p^, p^, p^, &c., inserted through
the barrel at right angles to its axis, now make the follow-
ing connections as seen in Fig. 170 ; the broad spring s^ is
connected with s'o, the spring Sg with s'g, &c., so that the
coils are connected in series, and a current entering the
instrument at the terminal p s leaves it by that marked
S, which is connected with s\2, having passed through all
the wires in succession.
The terminal s in the symbolical figures 169, 170 is
Chap. VIII.] COMMUTATOR AMMETER AND VOLTMETER. 431
drawn inside the wires in the position that the needle
would occupy in the actual instrument. This is merely
to prevent the wire which connects s with the spring
s'i2 having to cross the other wires, and so producing con-
fusion in the figures.
If all the coils were far away from the needle, and all
occupied practically the same position relatively to it,
the sensibility of the instrument when all tlie wires were
in series would hear to the sensibility when they were all
in parallel, a ratio simply equal to the number of separate
wires employed, quite independently of the way the cur-
rent divided itself among the wires when they were in
parallel. But if to obtain greater sensibility they be
wound on the bobbin close to the needle, some of them
will be, on the whole, nearer to it, and therefore have a
greater magnetic effect for the same current than the
rest, and it will be necessary, in order that the simple
ratio of the sensibilities given above shall exist, that the
current shall divide itself equally among the wires when
in parallel. For, since the same current passes, of course,
through each of the wires when they are in series, it
follows that, if matters be so arranged that equal currents
also pass through them all when in parallel, any particu-
lar coil will produce the same proportion of the total
magnetic effect whether the commutator be turned to
series or to parallel. Now, to insure that when the
commutator is turned to parallel, equal currents shall pass
through all the coils, it is necessary that they should be of
exactly the same resistance, and this, therefore, is the con-
dition fufiUed in constructing commutator instruments.
In the ammeter seen in Fig. 26, page 76, ten coils of
equal resistance have been wound on the bobbin, and
hence the ratio of the instrument in the two positions of
the commutator are as 1 to 10 ; the scale, therefore,
has two sets of graduations, the angular deflection on
the one to be used when the commutator is turned to
parallel, corresponding with ten times the number of am-
peres indicated by the other.
432 PRACTICAL ELECTRICITY. LChap. VIII.
The binding screws p and p s are made so that a thick
wire can be attached to them, while s has so small a
hole in it that only a fine wire can be put in it ; hence
the wires used to convey large currents, which come
from a dynamo machine, for example, can only be at-
tached to p and p s, and not to s, hence there is no fear
of either of them being attached to the wrong binding
screw ; and, further, as will be seen from Figs. 169, 170,
the strong current can only pass through the instrument
when the commutator is turned to parallel. Hence, even
if it be accidentally turned to series while the instru-
ment is connected with a dynamo, for example, or a large
battery of cells, the current will be interrupted instead
of being allowed to pass through all the coils in series,
which would probably burn them up, or would, at an^
rate, in consequence of the sensibility of the instrument
being increased, say ten times, knock the pointer violently
against the stops, which are inserted to limit its motion,
and damage it.
222. Calibrating a Commutator Ammeter. — First
plan : Turn the commutator to series so that only a
small current is required to produce a fairly large deflec-
tion, place the ammeter in series with a silver voltameter,
and calibrate by the method described in § 207, page 395.
Second plan : Turn the commutator to series, connect
the terminals of a cell of which the E. M. F. is known
accurately^ with the binding screws s and p s (Fig. 26,
page 76). Let it be E volts, and let a reading a^ on
the ammeter be obtained. Take out the plug, seen to
the left-hand side of Fig. 26, which has the effect
of introducing a resistance of one ohm into the circuit
when the commutator, as at present, is turned to series.
Let the reading on the ammeter be now a^. The am-
meter we will suppose to be so constructed that the
angular deflection is proportional to the current {see § 35,
page 71), and to have been originally direct-reading ; but
from the permanent magnet having become, say, weakened
since the instrument was adjusted, the readings are now
Chap. VIII.J CALIBRATING COMMUTATOR METERS. 433
too large, so that K times the reading gives the current
in amperes where K is a constant, less than unity, the
value of which we have to determine. If r be the re-
sistance of the cell, together with that of the instrument
(both of which may be unknown), when aB the coils
are in series, the current in the first case is
E
— amperes,
and in the second case
E
^r^ amperes,
•*• 7 = K«i.
and = K «„.
r + 1 ^
Eliminating the unknown resistance r, we have
K = E
%^2
The soft iron cores p (Fig. 27, page 77) should now be
adjusted until, on making the preceding experiment, K is
found to equal unity, when the instrument will be pro-
perly adjusted for both the "series" and "parallel"
scales (Fig. 26, page 76).
Of these two plans of calibration the first is more ac-
curate than the second.
223. Calibrating a Commutator Voltmeter. — A
voltmeter is more sensitive when all the coils are in
parallel than when they are in series ; hence, turn the
commutator to parallel, and attach to the proper binding
screws the terminals of a cell of known E. M. F. ; then,
if 6 be the resistance of the cell, and r that of the volt-
434 PRACTICAL ELECTRICITY. [Chap. VIII.
meter when all the coils are in parallel (both of which
resistances may be unknown), the P. D. maintained at
the terminals of the voltmeter will be
— ^ E volts {see § 128, page 224).
Remove the plug, which, in the case of a commutator
voltmeter, inserts a resistance equal to that of the in-
strument when all the coils are in parallel. The P. D.
maintained at the terminals of the voltmeter is now
2r
E volts,
2r + 6 • '
but the P. D. at the terminals of the coils of the volt-
meter, which is sending the current through them, is only
r
2r + 6
E volts.
Hence, if a-^ and a^ be the deflections produced in the two
cases on the direct-reading voltmeter, and if we suppose
that they require multiplying by an unknown constant
K to convert them into volts.
r
r
E = Kao,
2r + 6
. • . eliminating the unknown resistances r and 6, we
have
and, as in the case of the ammeter, the soft iron cores P
(Fig. 27, page 77) must be adjusted until K equals
unity.
Chap. VIII.l BEST RESISTANCE FOR GALVANOMETERS. 435
224. Best Resistance to give to a Galvanometer.
—The considerations given in § 217, page 418, enable us
to solve this question, for it was shown there that the
magnetic effect produced by the coils of a galvanometer
of given shape and size is proportional to G ^/^ where
G is the current flowing through the galvanometer, and g
the resistance of the coils. Our object, now, is to see
what should be the value of g^ or, in other words, what
gauge of wire should be used in winding the galvano-
meter, in order that G ^g may be a maximum. To
solve this problem we must consider what are the condi-
tions as to the rest of the circuit.
1st Let the circuit be a simple one, consisting of a
battery of fixed E. M. F. equal to E volts, and resistance
of h ohms in series with 2^ fixed resistance of r ohms, and
the galvanometer, then
h + T -\- g
The expression on the right-hand side is of the same
form as the expression in § 136, page 244, the s of that
expression being replaced by ^g in the above. Con-
sequently the value of ,/g that will make the above ex-
pression a maximum, can be found by giving fixed
numerical values to E and h + r, and then drawing a
curve similar to that shown in Fig. 93, page 245, having
for its abscissae values of ^g^ and for its ordinates the
corresponding values of
E .-
From this curve we should see that g equal toh -{■ r
makes the ordinate a maximum, and hence to obtain the
maximum magnetic effect with a galvanometer in a simple
circuity the gauge of wire wound on the coils of the
galvanometer should he such as will mxike the resistance
436 PRACTICAL ELECTRICITY. [Clmp. VIIL
of the galvanometer equal to that of the rest of the circuit.
When measuring, therefore, a resistance of many meg-
ohms by the method described in § 149, page 277, the
wire used in winding the galvanometer coils should be as
fine as can be conveniently wound on.
2nd. Let the galvanometer be a differential one, the
resistance of each of its coils being g ohms ; let the re-
sistance of the portion a (Fig. 59, page 149) be fixed
and equal to r ohms, and that of the portion b equal to
r -\- p ohms, p having a very small fixed value relatively
to r, since it is only when balance is nearly established,
and the deflection on the galvanometer is very small,
that it is of interest to determine what is the best value
to give to the galvanometer coils. Let E volts be the
E. M. F. of the battery inserted between the points P
and Q, and h ohms its resistance.
Then from § 137, page 253, the current through the
circuit A is
{r+g^p)^
6(2r + 2^ + p) + (r-f pr)(r + 5'+p)^'"^^'*^^'
and that through the circuit B is
h{2r^-2g-^p) + {r ^g){r + g +p)
amperes.
Hence the magnetic effect on the needle, which is equal
to the difference of the magnetic effects of the two
coils, is
p^^/g
6 (2 r -f 2 ^ + ;?) + (r + ^) (r + ^ + ;?)*
Since p is very small compared with r, this is approxi-
mately equal to
2 6 (r + i^) + (r + gf'
Cliap. Vin.] BEST RESISTANCE FOR GALVANOMETERS. 437
which may be written in the form
To determine the value of g that makes this a maxi-
mum, we may give fixed numerical values to p, E, r, and
6, and draw a curve. Generally, however, 6, the battery
resistance, is small compared with r and g, hence for all
practical purposes we may regard the magnetic effect on
the needle of a differential galvanometer as being ap-
proximately equal to the simple expression
(r + gy'
Drawing a curve with values of g for abscissae, and the
corresponding values of the expression for ordinates, we
find that the maximum ordinate corresponds with the
value of g equal to -k. Hence, to obtain the maximum
magnetic effect with a differential galvanometer^ the two
coils should be wound with such a gauge of wire that the
resistance of each of them, equals one-third of the resist-
ance to be tested.
3rd. Let the galvanometer be that used on a Wheat-
stone's bridge. This problem is more difficult to solve,
but the mode of determining the value of g that makes
the magnetic effect a maximum for a fixed small in-
equality in the ratios of the resistances of the pairs
of arms, is given in § 237, page 466, and the result has
already been indicated in § 98, page 172.
Example 104. — An ammeter has been constructed so
as to measure currents varying between 10 and 50 am-
peres, and it is desired, without altering anything but
the gauge of M^ire used to wind it, to adapt it to measure,
instead, currents varying between 3 and 15 amperes.
438 PRACTICAL ELECTRICITY. [Chap. VIU.
What should be the resistance of the instrument after
re- winding compared with its present resistance 1
Let a be the present resistance in ohms, and x the
required resistance after re- winding, then from § 217,
page 418,
3 y^ = 10 ^/a,
X _ 100
' * a ~ 9 *
Answer. — The resistance after re- winding should be
11-11 times the present resistance.
Example 105. — An ammeter so constructed that the
deflections are proportional to the currents, and having a
resistance of 0-0015 ohm, gives a deflection of 40° when
a current of 22 amperes passes through it. What should
be the resistance of another ammeter in every way
similar to the former one, except as to the gauge of
wire employed in winding the coils, so that it may be
direct-reading, degrees corresponding with amperes %
We wish that a deflection of 40° shall be produced
by 40 amperes instead of by 22 amperes, therefore, if x
be the required resistance in ohms,
40 v^ = 22 yO-0015,
.-. a; = 0-0004536.
Answer. — 453-6 microhms.
Example 106. — When a P. D. of 120 volts is main-
tained at the terminals of a certain voltmeter having a
resistance of 1,235 ohms, the pointer is deflected to the
end of the scale. The instrument has to be re- wound with
wire of such a resistance that the same deflection shall be
produced with a P. D. of 170 volts. What should be the
resistance after re- winding %
The current that deflects the pointer to the end of the
120
scale in the first case is amperes, and after re-winding
1} JuD
Chap. VIII.] EXAMPLES. 439
170
it will be amperes, if x be the new resistance of the
X
instrument in ohins, therefore
120 .Tl^ 170 .-
or
X
120 170
^/l,235 V^
Hence x = 2,477.
Answer. — 2,477 ohms.
Example 107. — With a voltmeter wound according
to a certain law as regards variation of thickness of wire
with the radius of the convolution, and having wire 0*012
of an inch thick for the innermost convolution, the pointer
deflects over the portion of the dial that is graduated
when the P. D. varies from 30 to 150 volts. If the in-
strument be re- wound according to the same law, but with
the innermost layer consisting of wire 0*015 of an inch
thick, what will be the range of the instrument 1
If r be the resistance of the voltmeter before re-wind»
ing, and r' that after ve- winding.
r V 0-015/'
and if V be the P. D. in volts required to deflect the
pointer to the higher end of the scale after re- winding,
V _ 150
^0*012y
= 96 volts.
V=/^^-?-L2Vxl50
VO-015
440 PRACTICAL ELECTRICITY. [Chap. VIII.
Similarly the P. D. corresponding with the lower end of
the scale will be
fO^y^ 30, or 19-2 volts.
V 0-015/
Answer. — After re -winding, the range of the voltmeter
will be from 19-2 to 96 volts.
Example 108.— When a P. D. that will deflect the
pointer to the end of the scale is maintained at the ter-
minals of a voltmeter, it is found that, due to the heating
of the coil by the passage of the current, the reading
diminishes by 5 per cent, at the end of a considerable
time. If the resistance of this voltmeter be 100 ohms,
and if, instead of using the voltmeter alone, it be put in
series with an outside resistance of 1,000 ohms made of
platinoid wire, by how much per cent, will the voltmeter
reading fall off on account of the heat produced, when the
platinoid wire is of such a thickness that its resistance is
only increased by -j^th per cent, on a current being kept
for a considerable time passing through it strong enough
to deflect the voltmeter pointer to the end of the scale 1
When the pointer is deflected to the end of the scale,
the voltmeter resistance increases by 5 per cent., that is,
from 100 to 105 ohms, while the resistance of the out-
side coil of platinoid wire increases by only -^j^th per cent.,
that is, from 1,000 to 1,001 ohms. Therefore the total
increase of resistance is from 1,100 to 1,106, or an in-
crease of 0'55 per cent.
Answer. — With the outside resistance the maximum
deflection will fall off by 0*55 per cent.
Example 109. — If the voltmeter referred to in example
106 be re- wound so that the pointer is deflected to the
end of the scale when a P. D. of 3 volts is maintained
between the voltmeter terminals, by how much will the
E. M. F. of an accumulator having a resistance of 0*001
of an ohm appear to be lowered if it be measured with
the voltmeter so re-wound 1
Chap. IX.] POWER. 441
Let X ohms be the resistance of the vo/fcmeter after
re-winding, then
3 _ 120
^/x \/l235'
.-. a; = 0-7716.
If E volts be the E. M. F. of the accumulator, and V
the P. D. between its terminals when they are joined bj
the voltmeter, then
0-7716 + 0-001
Answer. — The E. M. F. is diminished by 0-12 per cent.
CHAPTER IX
POWER AND ITS MEASUREMENT.
225. Power — 226. Watt — 227. "Wattmeter — 228. Distribution ot
Power in a Circuit— 229. Ciirrent that Develops the Maximum
Useful Power — 230. Efficiency— 231. Measuring the Efficiency of
an Electric Light — 232. Dispersion Photometer — 233. Efficiency
and Life of Incandescent Lamps.
225. Power. — " Power " is the name given to the
rate of doing work^ and it must be carefully distinguished
from the amount of work done, there being the same
sort of difference between power and work^ that there is
between a velocity and a distance. When a constant
current is flowing through a circuit, at the terminals of
which a constant P. D. is maintained, the power given to
that circuit and expended in its circuit is constant, and
is measured by the ratio of the work done in any time,
442 PRACTICAL ELECTRICITY. [Chap. IX.
divided by the time in which the work is done. If,
however, either the current or the P. T>. be fluctuating,
the power is also varying in amount, and the rate of
doing work at one moment is greater or less than that at
a subsequent one. In such a case we mean by the power
expended at any moment, not the actual work done in a
minute or even in a second, but the following : — Measure
the work done in a very short time, a portion of which
precedes, and the remainder of which follows the in-
stant at which we wish to measure the power, divide
the work done in the very short time by that time, then
the ratio more and more nearly represents the power
being expended at the moment in question as we make
the very short time shorter and shorter.
Whether, however, the power given electrically to a
circuit and expended in it be constant or not, it is very
easily measured, for the work done in t minutes in a
circuit through which A amperes flow, and at the ter-
minals of which a P. D. of Y volts is maintained, is
44-25 AY t foot pounds
(see § 114, page 201), therefore it follows that the power,
measured in foot pounds per minute, equals
44-25 AV;
or, measured in foot pounds per second, equals
0-7375 A V;
or, measured in horse-power, equals
^or 0-00134 AV,
746
A and V being the amperes and volts obtained by a
simultaneous measurement of the current and P. D.
Chap. IX.] THE WATT. 443
226. Watt. — A " watt " is the power developed in a
circuit when one ampere flows through it, and when the
P. D. at its terminals is one volt, hence the number of
watts developed in any circuit equals the product of the
current in amperes flowing through it into the P. D. at
its terminals in volts. Therefore
1 watt is the power developed when 44-25 foot
pounds are done per minute.
1 watt is the power developed when 0*7375 foot
pounds are done per second.
1 watt equals ttq^^ o^ ^ horse-power.
Example 110. — If an incandescent lamp give an
illumination of 16 candles when 0*7 ampere passes
through it, and 110 volts are maintained at its terminals,
how many watts are required per candle ?
Answer. — 4*8.
Example 111. — How many watts must be expended
to send a current of 5 amperes through a resistance of
10 ohms'?
If V be the P. D. maintained at the terminals of the
resistance,
V = 5 X 10,
. • . the power = 5 x 50.
Answer. — 250 watts.
This question may also be solved thus : — If a circuit
consist simply of a conductor of resistance r ohms, and
in which there is no E. M. F., so that the power is simply
expended in heating the conductor, the work done in t
minutes equals
44-25 A2r«
{see § 114, page 201). Hence, in such a case, the number
of watts equals
A2r.
444 PRACTICAL ELECTRICITl?. [Chap. IX.
Hence, in the present example,
the power =25 x 10.
Answer. — 250 watts.
Example 112. — If each incandescent lamp require
3 watts to make it glow properly, how many such lamps
can be illuminated by the expenditure of one horse-power
in the circuit ?
Answer. — 248 lamps if a very little too bright, or
249 if a very little too dull.
Example 113. — If an electric horse-power cost £15
per annum for 5 hours per night, what is the value of
one watt-hour?
One watt being the y^th part of a horse-power,
and one hour the ^ ^^ gth part of the time during
which the horse-power is supplied, it follows that the
value of one watt hour is
15
or about the xJit*^ of a farthing.
227. Wattmeter. — The watts being expended in any
circuit can, as we have seen, be ascertained by a simul-
taneous measurement of current and P D., and since we
generally desire to know the current and the P. D. as
well as the watts, the simultaneous measurement of the
two former is usually employed to give us the latter. By
the employment, however, of a " wattmeter" it is possible
to measure the watts directly. This instrument consists
of two coils, one of thick wire placed in the main circuit,
like c (Fig. 71, page 190), and therefore traversed by the
whole current, the other oifine wire put like c, as a shunt
to 0, the part of the circuit in which we wish to ascertain
the expenditure of power. Instead, however, of the cur-
rents passing through these two coils acting on a needle as
they do in the ohmmeter, they act on one another in a
wattmeter in the same way as do the currents flowing
Chap. IX.] WATTMETER. 445
through a Siemens' dynamometer (§ 199, page 377). In
fact, if one of the coils in a Siemens' dynamometer be
made of fine wire, and if instead of the two coils being
connected in series with one another they be placed as
are the coils c and c relatively to o (Fig. 71, page 190),
the instrument becomes a wattmeter, for the couple mea-
sured by the rotation of the pointer m (Figs. 151, 152,
pages 379, 380) will, in this case, measure the product
of the whole current passing through o into the P. D.
maintained at its terminals — that is, the number of
watts expended in o.
Instruments of this kind have been made by M.
Deprez, the author. Sir William Thomson, and the late
Sir William Siemens.
The main error in wattmeters is the heating error
that occurs in voltmeters (see § 212, page 407), and it
may be overcome by using the same means as are em-
ployed for obviating this defect in voltmeters (see § 218,
page 421).
228. Distribution of Power in a Circuit. — Of the
power developed by a current generator, say P watts,
when it is sending a current through an external circuit,
one portion, say P;^ watts, is wasted in heating the gene-
rator itself, and the remainder, say Pg watts, is utilised
in the external circuit. And in all cases
P is equal to the product of the current, in amperes,
into the E. M. F. of the generator, in volts.
Pj is equal to the product of the square of the current,
in amperes, into the resistance of the generator,
in ohms.
Pg is equal to the difference between P and P^.
If the outside circuit consist simply of a conductor
having resistance, but containing no voltameters nor
electromotors in motion — in fact, nothing that can pro-
duce an E. M. F. — the power P developed by the generator
will be divided between the generator and the outside
446 PRACTICAL ELECTRICITY. [Chap. IX.
circuit directly as their resistances, so that, if R be the
resistance of the generator, and r that of the outside
circuit,
and Po = ^
2
r + R
But if there be an E. M. F. in the outside circuit, then
neither of the two last equations will be true, hut in all
cases the three relationships given above will hold — that is,
if the E. M. F. of the generator be E volts,
P =AE,
Pi = A2R,
P2 = AE-A2R
= A(E-AR).
Example 114. — A battery consisting of 4 Daniell's
cells in series, and 2 in parallel, is employed in sending a
current through a simple conductor, having a resistance
of 2 ohms. If the E. M. F. of each cell be 1 • 07 volts, and
the resistance 0-8 ohm, how many watts are developed
by the battery, how many are employed in heating the
external resistance, and how many are wasted in heating
the battery 1
The current produced =
2 + ^ X ^'^
2
= 1*189 amperes ;
the power developed by ) _ j.-^gg ^ ^.gs
the battery J
= 5-089 watts;
Cliap. rXJ EXAMPLES. 447
the watts employed in J „
heating the external > = — ^ 5*089
resistance I 3*6
= 2-827 watts ;
the watts employed in ) _ 5.oq9_ 2-827
heating the battery ) ~
= 2-262 watts.
Example 115, — What must be the resistance of a
current generator so that 95 per cent, of the power pro-
duced by it shall be given to the outside circuit, consist-
ing of a simple conductor having a resistance of 35
ohms?
We have = — ,
35 + R 100
if R. be the resistance of the generator ;
.-. R = 1-842.
Answer. — 1*842 ohms.
Example 116. — If a Cardew's voltmeter be used to
measure the P. D. of the incandescent lamp referred to
in example 110, how many watts are absorbed in the
voltmeter, and what is the ratio of the watts absorbed in
the voltmeter to the watts used in the lamp 1
From Table I., page 154, we see that the resistance
at 0°C. of 13 feet of platinum-silver wire 00025 of an
inch in diameter is
9-603 X 13 X 12 X 4 . ,
microhms,
TT X 0-00252
or if we assume that the resistance is increased by 5 per
cent, by the elevation of temperature, the resistance will
448 PRACTICAL ELECTRICITY. [Chap. IX.
be 319 ohms Therefore the number of watts absorbed
in the voltmeter equals
i^^or 37-93 watts.
319
The number of watts used in the lamp is 77, therefore
about half as many watts are absorbed in the voltmeter
as are used in this lamp.
229. Current that Develops the Maximum Useful
Power. — The power used in heating a current genera-
tor is generally entirely wasted, and, in addition, if
allowed to become excessive, will prevent the generator
working properly, whereas all the power given to the
outside circuit may be utilised with proper arrangements.
The problem of ascertaining the current that will develop
maximum useful power may be solved either on the
assumption that the generator is fixed and the external
circuit variable, or on the assumption that it is the exter-
nal circuit that is fixed, and the generator is the thing to
be varied.
1st. Let the generator have fixed values of E and R
(which will be the case for a battery, a set of accumula-
tors, or a magneto-electric machine running at a constant
speed, but not usually for a dynamo machine), then the
equation
P2 = A(E-AR)
shows us that we must determine the value of A that
makes this expression a maximum, in order to find the
current that develops the maximum useful power. To
do this, give numerical values to E and E-, and plot a
curve, having the values of A for abscissae, and of Pg
for ordinates. Such a curve is shown in Fig. 171, the
values of Pg being calculated on the supposition that E
and R are equal to 2 and 3 respectively, and it will be
seen that the value of A that makes Pg a maximum is
A = -^
2B'
Chap. IX. J
MAXIMUM USEFUL POWER.
449
that is, a current generator having a fixed E. M. F. and
resistance gives maximum power to the external circuity
when that circuit is such that the current that flows is
half the current that woidd flow if the generator were
short-circuited.
We do not say that the conductor must have a resist-
ance equal to that of the generator, since, although this
will undoubtedly reduce the current to one-half if the out-
side circuit be a simple conductor, there are other ways of
reducing the current to one-half, such as the insertion of
an opposing E. M. F. equal to half that of the generator.
When A has the value given by the last equation,
P =
E2
2R
DD
450 PRACTICAL ELECTRICITY. LCliap. IX.
p - ^"
and Pg =
4R
E2
4R
therefore, with a current generator having a fixed
E. M. F. and resistance, maximum power will he given to
the outside circuit when the power developed hy the gene-
rator is expended half in the outside circuit and half in
heating the generator itself
On the other hand, maximum power will be deve-
loped by the generator when maximum current flows
through it — that is, when the generator is short-cir-
cuited.
2nd. Let the exteinal circuit consist of a simple con-
ductor, and let its resistance be fixed and equal to r
ohms ; also let the current generator be a battery con-
sisting of a fixed number of cells N, each having an
E. M. F. of e volts, and a resistance of h ohms. Then,
since the power developed in the external circuit equals the
square of the current into r, and since r is a constant, it
follows that the arrangement of cells that will give
maximum power to the external circuit, is that which
will produce the maximum current. Now, this arrange-
ment we have seen (§ 136, page 245), is that which
makes the resistance of the battery equal to the ex-
ternal resistance. Hence, the arrangement of a given
number of cells that gives maximum power to a simple
conductor having a fixed resistance, is that which makes
tlie resistance of the battery equal to the resistance of the
conductor.
With this arrangement of cells, it is easy to see that
the power developed by the battery will be twice that
given to the external circuit, one-half being wasted in
heating the battery. But this arrangement of cells will
not, as a rule, make the power developed by the battery
Chap. IX.1 EFFICIENCY. 451
a maximum. For, as shown in § 136, page 244, the cur-
rent equals
se
— - amperes,
, 8^ 0
r -f
N
and, therefore, the power developed by the battery-
equals
8^e^
r -\
N
watts,
which equals watts,
r b
S2 + N
and this obviously has its least practical value when s
equals unity, that is, when all the cells are in parallel,
and has its largest practical value when s equals N, that
is when all the cells are in series. Hence, if the resist-
ance of the outside circuit be less than that of the
battery, putting all the cells in series will not only give
less power to the outside circuit than if the cells be so
arranged that the battery resistance is equal to that of
the outside cii-cuit, but it will waste much more power,
since the total power produced by the battery will be
greater.
230. Efficiency. — The " efficie^icy " of a system con-
sisting of a current generator supplying power to an out-
side circuit, is the ratio of the power given to the outside
circuit to that developed by the generator.
From the equations P = A E,
P2= A(E-AR),
we see that in all cases the efficiency equals
E-AR
452 PRACTICAL ELECTRICITY. [Chap. IX.
hence, the efficiency will be the greater the larger we
make E, and the smaller we make A and R.
From § 229 we see that if we wish a current genera-
tor having a given E. M. F. and resistance to develop as
much power as possible in the outside circuit, we arrange
matters so that the current is half that which would be
produced if the generator were short-circuited, or, what
is the same thing, so that half the power is wasted
in the generator itself ; hence, when a Grove's battery is
employed to produce a bright electric light, we regulate
the lamp so that the P. D. at its terminals is half the
E. M. F. of the battery. Whereas we have just seen
that if we wish a current generator to give power econo-
mically to the outside circuit, we employ a generator
having a very large E. M. F., and allow it to produce only a
small current ; hence, in the recent electric transmission
of 50 horse-power by M. Deprez from Creil to Paris, a
distance of about 37 miles, he employed an E. M. F. of
between 6,000 and 7,000 volts, and a current of only 10
amperes.
231. Measuring the Efficiency of an Electric Light.
— The ^^ efficiency of an electric light" is the ratio of the
illuminating power of the light to the watts supplied to it.
To measure the illuminating power we use a "photo-
meter,^^ the simplest, and at the same time one of the
most accurate, being that designed by Rumford. A form
of " Rumford^ s photometer" is seen in Fig. 172, e being
the electric light, an incandescent lamp, for example, held
in a convenient adjustable holder h, and c a " standard
candle^' which is a special form of candle made so as to
bum 120 grains of spermaceti wax per hour."* The
lamp is placed at a convenient distance e from the
screen s, which is covered with a sheet of white blotting
* For rough experiments on illuminating power, No. 8 sperm
candles, costing lid. per pound, may be used satisfactorily instead of
standard candles costing 2s. 9d. per pound, since experiments show
the No. 8 sperm candles do not differ much more from one another, or
from a standard candle, in illuminating power, than standard candles
are said to differ among themselves.
Chap. IX.]
EFFICIENCY OP ELECTRIC LIGHT.
453
paper, and the candle is moved backwards and forwards
along the graduated arm g g, until, by trial, a position for
it is found, at a distance, c, say, from the screen, such
that the two shadows cast by a vertical rod of blackened
wood R, about the thickness of an ordinary pencil, and
fixed at about two inches from the screen, appear to
Fig. 172.
be equally dark. Under these circumstances, as the
portion of the screen not in shadow is illuminated by
both sources of light, whereas the two parts in shadow
are each illuminated by only one, and as the screen s and
the rod r are so placed that lines drawn through the
rod and through each of the lights make equal angles
with the screen, it follows that, when the shadows are
equally dark, the quantities of light falling on a square
inch of the screen, due to each of the lights, are equal to
one another, hence
the illuminating power of the electric light
» ,, ,, ,, standard candle
454 PRACTICAL ELECTRICITY. [Chap. IX.
The correct position of the candle which produces
equality in the darkness of the shadows can be best
detected not by gradually moving the candle continuously
towards or away from the screen, but by trying to find a
position such that, if the candle be put a little nearer, one
of the shadows becomes distinctly too dark, whereas if
it be put a little farther away, that one of the shadows
becomes distinctly too light.
The current passing through the lamp is measured
by an ammeter A, and the P. T>. maintained at the lamp
terminals by the voltmeter v, the product of the amperes
and the volts giving P, the watts furnished to the lamp.
Hence, the efficiency of the lamp equals
C2P'
232. Dispersion Photometer. — In the preceding sec-
tion we have spoken of one type of electric lamp — the
incandescent one. This consists of a hermetically sealed
glass bulb (see note, § 10, page 20) containing usually a
very fine filament of carbon, which becomes luminous
when a suitable current passes through it, but does not
burn away as there is a very perfect vacuum inside the
glass bulb. But there is a much more powerful electric
light — the arc light, in which the light is produced by
a current passing between two pieces of carbon slightly
separated from one another, the resistance of the heated
air between the carbons taking the place of that of the
carbon filament in the incandescent lamp. As an arc
light has often an illuminating power of several thousand
candles, it would have to be put many feet away from
the screen of the photometer in order that the light cast
by it on a given area should be equal to that produced
by the standard candle. To avoid the inconvenience of
having to put an arc light so far away from the screen,
the '^ dispersion photometer " shown in Fig. 173 was de-
vised by the author. Instead of the light from the
CLap. IX.J
DISPERSION PHOTOMETER.
455
electric lamp being allowed to fall directly on the screen,
it is allowed to pass through a double concave lens L,*
which disperses the light, so that the screen is illumi-
nated by only a small fraction of the light that would
come to it from the powerful electric lamp if the lens l
Fig. 173.
were removed. Let the electric light and the lens be at
distances e and I respectively from the screen, and, when
the standard candle is at a distance c from the screen, let
the shadows be equally dark, then the light from the
electric lamp which would have illuminated an area A
(Fig. 174) is now dispersed so as to illuminate a much
larger area A', so that
the illuminating power of the electric light A' e^
„ „ „ „ standard candle A c^
To find the ratio of A' to A, let a be the area of
* Dr. J. Hopkinson uses a double convex lens, and forms a real
image of the electric arc between the lens and the screen.
456
PRACTICAL ELECTRICITY.
[Cbap. IX.
the double concave lens filled by the pencil of light
which would have illuminated the area A, and let the
Fig. 174.
light after dispersion appear to come from a distance x
behind the lens, then
A e2
a {e-lf
A' _\l-\-xf
and
_ Ae - I)
~f+e-l
where / is the ^' focal length " of the lens — that is, the
distance from the lens of the point from which light,
after passing through the lens, would appear to come if
the source of light were very far away, like the sun.
Hence, eliminating a and x from the preceding three
equations, we have
the illuminating power of the electric light
fi „ „ ,, standard candle
< of
}•
Chap. IX.] DISPERSION PHOTOMETER. 457
A great difficulty in comparing an electric light with
a candle arises from the difference in colour of these two
sources of light, an arc light being much bluer than a
candle. To partially overcome this difficulty, two dis-
tinct comparisons of the electric light with the candle
should be made when the screen is looked at succes-
sively through green and red glass. Pieces of what are
known in the trade as signal green and ruby red answer
very well for this pui-pose, but they should be selected so
that a bright light is hardly visible when looked at through
the two pieces placed one over the other, as then the
green glass allows practically no red, and the red glass
practically no green light to pass. The two comparisons
made with green and red glass will give very different
results for the illuminating power of a powerful arc light
in terms of that of a candle, because the ratio of green
to red rays in the former is so much larger than in the
latter.
It is important to be able to measure the illuminating
power of an arc lamp, not merely in a horizontal plane,
but for rays making various angles with the horizontal.
This can be conveniently done by placing the arc lamp
so that its rays come in any desired direction to the
mirror M (Fig. 173), and turning the mirror, with the gra-
duated disc D attached to it, until the rays pass through
the concave lens l, and fall properly on to the screen s.
The angle that the beam of light under observation now
makes with the horizontal plane at the electric light,
can be read off directly by the position of the graduated
disc. By causing the mirror m to turn about an axis
which makes an angle of 45° with its plane, the light
reflected from it always makes the same angle with its sur-
face when it passes after reflection through the lens, hence
the portion of the light absorbed by the mirror is con-
stanty and may be determined once for all experimentally.
So also the portion of the light absorbed by the lens will
be constant, and may be determined experimentally, and
both these fractions can easily be allowed for in any
458 PRACTICAL ELECTRICITY. [CLap. IX.
measurements made of the illuminating power of an arc
lamp.
233. Efficiency and Life of Incandescent Lamps. —
The heat produced per second in a conductor is propor-
tional to the square of the current passing through it
{see § 113, page 198), and is therefore proportional to the
product of the current into the P. D. maintained at
the ends of the conductor — that is, to the number of watts
given to it. The temperature of the conductor will de-
pend on the heat produced in it per second, and on its
facility for cooling {see § 1 1 1, page 1 95). But experiments
show that the light emitted by a body increases very
much more rapidly than the heat given to it per second ;
for example, the heat given to a kettle of boiling water
per second may be considerable, but is not sufficient to
cause the kettle to emit any light at all, whereas if the
metal of the kettle be made a good deal hotter, it will
begin to glow and commence emitting light, and when it
becomes white-hot, the light emitted will be considerable.
So it is found that the light emitted by an electric lamp
increases much rnore rapidly than the watts given to it —
that is, the efficiency increases with the power supplied to
it. As far then as the cost of producing the power is con-
cerned, it is more economical to cause the carbon of an
electric lamp to have an intensely white-hot temperature
than merely to allow it to glow at a dull red heat. But,
on the other hand, the number of hours during which an
incandescent lamp can be used before the carbon filament
breaks, depends on the temperature of the filament. If
the temperature be kept always low enough, the filament
will last for several thousands of hours, the lamp emitting
light all the time, whereas if the temperature be too high,
the life will be reduced to a few hundred, or less number
of hours. Hence it is an important question to decide
how bright we should make the filament of an incandes-
cent lamp when in use, or, in other words, what P. D. we
should maintain at its terminals. This question is one
that must be solved for each particular case, depending on
Chap. IX.] EFFICIENCY AND LIFE OF LAMPS. 459
the efficiency and life of the lamp for different P. Ds.,
on the cost of a new lamp, and on the cost of power
at the particular place where the lamp is used.*
Example 117.— If power cost £15 per horse-power
per annum supplied for 5 hours per night, and if a new
incandescent lamp cost 3s., further, if when used so as
to require only 2^ watts per candle it lasts for 500
hours, whereas when used with a lower P. D. at its ter-
minals it requires ?>\ watts per candle, but lasts 1,500
hours, determine which is the more economical of the
two modes of using the lamp 1
First case : —
Cost for ^oi(;er per candle _ 15 x 20 x 21 ,.,,.
per hour ~ 746 x 5 x 365 ^ ^"^^
Cost for lamp renewals per 3
candle per hour = ^ shilhngs,
TotaUost per candle per ^ ^,^^^^^ ^^^^^^^^
Second case : —
Cost for ^ower per candle _ 15 x 20 x 3^ ,.,,.
per hour ~ 746 x 5 x 365 ^ ^^^*
Cost for lamp renewals per 3
candle per hour " Yg^ ^^^^^'^^s,
Totd cost per candle per ^ ^.^(^^72 shillings,
therefore using the smaller P. D., and the larger number
of watts per candle, is much the more economical arrange-
ment.
Eocample 118. — An arc lamp through which 8 am-
peres are passing, and at the terminals of which 50 volts
* See * ' The Most Economical Potential Difference to employ with
Incandescent Lamps." PhU. Mag.^ April, 1885.
460 PRACTICAL ELECTRICITY. [Chap. IX.
are maintained, produces 750 candles, while an incandes-
cent lamp through which 0*6 of an ampere is passing,
and at the terminals of which 70 volts are maintained,
produces 17 candles. Compare the efl5ciency in the two
cases.
750 or about 1 • 9 candle
For the arc lamp the efficiency is g-^- p^^. ^^tt.
For the incandescent lamp the 17 or about 0-45
efficiency is 0'6 X 70 candle per watt,
therefore the efficiency of the arc lamp is more than four
times that of the incandescent.
Example 119. — A battery having a resistance of 4
ohms, and an E. M. F. of 30 volts, is sending a current
through an outside circuit consisting of leading wires
having a resistance of 1 ohm and 4 incandescent lamps
arranged in parallel, and at the terminals of which 12
volts are maintained. If each lamp produces 3|^ candles,
calculate the efficiency of the an-angement.
rrv. *. 30 - 12
The current =
4+ 1
= 3*6 amperes.
The power produced by the battery = 3 6 X 30
= 108 watts.
The power wasted in the battery = (3-6)'' X 4
= 51-84 watts.
The power wasted in tho leading wires = (3*6)^ X 1
= 12-96 watta
Chap. IX. 1 THE JOULE. 461
The power given to the 4 lamps in _ o.n ^ in
parallel
= 43-2 watts.
Therefore, of the 108 watts produced by the battery,
64-8 watts, or 60 per cent., are spent uselessly in heating
the battery and leading wires; 43 -2 watts, or 40 per
cent, of the total power, are given to the lamps ; and, as
4 X 3| or 14 candles' illumination is produced, the effi-
ciency of the lamps is 0*324 candles per watt.
When a power of 1 watt is being developed the work
done per second is sometimes called a "joule." Hence
1 joule equals 0-7375 foot pounds. And
1 watt-second = 1 joule.
1 watt-minute = 60 joules.
1 horse-power hour = 1,980,000 foot pounds.
„ „ „ - 2,685,600 joulea
462
Appendix to the Section on Shunts.
234. Kirchhoff's First Law— 235. Kirchhoff's Second Law— 236.
Current through the Galvanometer of a Wheatstone's Bridge —
237. Best Resistance for the Galvanometer with a Wheatstone's
Bridge — 238. Best Arrangement of the Battery and Galvanometer
with a "Wheatstone's Bridge — 239. Measuring a Resistance contain-
ing an E. M. F.
In the case of even a somewhat complicated circuit
like that shown in Fig. 175, there is no difficulty in cal-
culating the current flowing in every part, if we use the
principles developed in § 103, page 177, and in § 137,
page 253, to solve the problem step by step. Let capital
letters stand for the currents flowing in the several
branches, and small letters for the resistances of these
branches ; let x be the resistance between the points 1
and 2, and y that between 3 and 4, and let E be the
E. M. F. of the battery ; then
a; = ^
g ^-s
_ t{x-\- t)
CALCULATING CURRENTS IN COMPLEX CIRCUITS, 463
B =
T =
E
b+p + q -\-y'
R
G =
X -{■ r -\- t
t
X -\- r -\- t
s
B,
s + ff
S= ^
R,
K
s + 9
Hence, the currents B, T, R, G, and S are expressed in
terms of E, and the various resistances b, j), q, i, ^, ff, and s.
But if we try to do the same thing for the circuit
shown in Fig. 176, and which at first sight appears
Fig. 176.
equally simple, it will be seen that the method previously
employed is inapplicable. We may say that
E
B =
h -f- resistance between 1 and 4
464 PRACTICAL ELECTRICITY.
but how are we to express the resistance between the
points 1 and 4 in terms of p, q, r, s, and gr. To do this
we require to use what are known as " Kirchhoff^s first
and second laws."
234. Kirchhoffs First Law. — This is very simple,
and merely expresses the fact that if there is one current
B (Fig. 176) that flows towards a point 1, and two
currents P and Q that flow away from this point
B = P + Q . . . . (1)
Similarly, P = G+ R . . . . (2)
S = G+Q . . . . (3)
B = R+S
These equations are not, however, all independent,
as any one could be obtained from the other three.
Kirchhoff'^s first law is sometimes stated thus : — TJte
algebraical sum of all the currents meeting at a point is
nought, the " algebraical " sum meaning that the currents
that flow away from the point must be taken with a
tiegative sign if those flowing towards it be taken with a
positive sign, or vice versct.
235. Kirchhoff's Second Law. — In any closed cir-
cuit the algebraical sum of the products of the currents into
the resistances equals the E. M. F. in the circuit. In using
this law the currents are to be taken with a positive or a
negative sign according as they flow in the same or in
opposite directions round a circuit ; and the E. M. F. is
to be taken with a positive or a negative sign according
as it assists or opposes the currents that are arbitrarily
taken as positive.
Let V^, Vg, V3, &c., be the P. Ds. at the points
1, 2, 3, &c., then from Ohm's law (see § 74, page 130) it
follows that
P;, = V, - V^,
Gg=Y,- V3,
Qq= V1-V3,
KIRCH hoff's laws. 465
Similarly, Rr = Y^ - Y^,
Ss z= Yg-V^
. •. G^ + Ss-Rr = 0 . . . . (6)
As to the circuit containing the battery and the points
1,3,4,
Q^= Vj- V3,
S. = V3-V„
B 6 = E - (Yi - Y4), (see § 116,
[page 205).
.'. Qg+ Ss + B6 = E . . . . (6)
Three independent equations (1), (2), (3), therefore,
may be obtained by using Kirchhoff's first law, and three
more (4), (5), (6), by using his second law, or six equa-
tions altogether. From these the six currents B, P, Q, R,
S, and G can be found in terms of E, the E. M. F. of the
battery, and the six resistances b, p, q, r, s, and g.
236. Current through the Galvanometer of a
Wheatstone's Bridge. — The current of most interest to
us is G, because this is the current that will pass through
the galvanometer in a Wheatstone's bridge when balance
is not obtained. The value of G"* so obtained is
'E(qr — ps)
f>{9(p-\-q-hr-^ s)-\- (p + q) (r -\-s)} +g(p+ r){q + s)
•\.r{p -hq){q -hs) - q (q r - p s)
And this we see equals nought when
qr = ps,
* A very convenient method based on Kirchhoff's laws, but in-
volving the use of determinants for solving such questions, was sug-
gested by the late Professor Clerk Maxwell, and has been recently
extended by Dr. Fleming in the Proc. Phys. Soc, voL vii., part 3,
page 215.
B E
466 PRACTICAL ELECTRICITY.
i.e. when ^ = -
q 8
This result for the law of the Wheatstone's bridge was
touch more simply obtained in § 97, page 167, but the
method there employed for arriving at the connection
that existed between the resistances when no current was
passing through the galvanometer, gave us no indication
as to what the current would be if this connection between
the resistances were not fulfilled. If qr equals p s there
will be no current through the galvanometer, whatever be
its resistance, or however it be constructed ; but as our
only method of insuring that qr shall be equal to ps^ is by
varying one or more of the resistances until no visible de-
flection is observed on the galvanometer, it is important to
construct the galvanometer so that the needle will deflect
even when there is a very small difference between q r
and p s. The proper wire to wind on the galvanometer
bobbins may be calculated from the formula given in
§ 98, page 171 ; and that formula, as will be seen in the
next section, can be obtained by multiplying the ^'g
(which we know from § 217, page 418, is proportional
to the sensibility of the galvanometer) by the value of G
given above when qr — ps has a fixed small value, and
seeing what is the relationship between g and p, q, r,
and s that makes G ^/g a maximum.
237. Best Resistance for the Galvanometer with a
Wheatstone's Bridge. — If G be the current passing
through the galvanometer of a Wheatstone's bridge, and
g be its resistance, the magnetic effect, which is propor-
tional to G ,/g~ is, from the last section, proportional to
E (qr-ps) yg ^
b (j) + q) {r + s) + r (p -\- q) {q -\- s) - q {qr - ps) _
+ {b(p-\-q + r-\- s) + (p-\-r){q-\- s)}
Now this expression is of the form
ax
BEST RESISTANCE FOR BRIDGE GALVANOMETER. 467
where a, 6, and c are constants, and x is the variable,
and such an expression we saw in § 136, page 245, is a
maximum when
c
Therefore it follows that G ^g will be a maximum when
_ h{'p^(i){r •\-8) ■\- r{jp -\-q){q^s) — q{(iT — 'p8)
^ ~ 6 (;> -f 5' + r + s) + (;? + r) (5^ + «)
But we want to find the best value to give to g when
balance is nearly established, that is, when g r is nearly
equal to p s, since that is when it is most important to
have the galvanometer sensitive, hence we may assume
that q r equals p s iu the preceding expression for g.
Under these circumstances we find that
_ bq(r + sf -\- qr (r -\- s) (q + s)
^ ~ b(r + s){q -\-s) -\-r(q-^sf
_ r + 8 ^ b (r -\- s) -\- r (q -\- s)
q.+ 8 b {r -^ s) -\- r (q -\- s)
And this when q r equals p s is the same as
(p + q) (r + s)
P + q + r + 8*
which is therefore the best resistance to give to the gal-
vanometer.
238. Best Arrangement of the Battery and Galvano-
meter with a Wheatstone's Bridge. — We have seen, in
§ 97, page 167, that when balance is obtained the battery
and galvanometer may be interchanged without disturbing
the balance. But when balance has not been obtained
a greater current will pass through the galvanometer when
it and the battery are arranged one way than will pass
when the galvanometer and the battery are interchanged.
468 PRACTICAL ELECTRICITY.
In other words, one arrangement is more sensitive than
the other, and the object of the following is to ascertain
which is the more sensitive arrangement.
As we are dealing with a deJ&nite galvanometer of
fixed resistance, we are merely concerned with the current,
and need not consider the magnetic effect. Let G^ be
the current passing through the galvanometer when it
and the battery are placed as shown in Fig. 176, page
463, and let G^ be the current when the galvanometer
and battery are interchanged, then
^ ^ ^(qr-ps)
^ ^{9iP +q+ri-8) + {p + r)(q-\-s)}
■^ 9 (P -^ q) {'^ -\- s) + p {q + s) (r + s) — s (ps — qr)
and the value of G^ is given in § 236, page 465.
Hence
a a -Mq^-ps) (^_j,\^ {p-\-q){r-^s)i
^'^' D;^^^^ ^^l-{P^r)(q+s)i
where Dj and Dg stand respectively for the denominators
of Gj and G3. Simplifying, we have
1st. — Let g he greater than b. Then G;^ — Gg will be
positive, that is, the first arrangement will be more sen-
sitive than the second, when p and r are respectively
both greater or both less than s and q. Therefore the
galvanometer should connect the junction of the two greater
resistances with the junction of the two less.
2nd. Let b be greater than g. Then Gj — G^ will be
positive, or the first arrangement will be more sensitive
than the second, when p is greater than s, and r is less
than q, or when p is less than s, and r is greater than q.
Therefore the battery should connect the junction of the
two greater resistances with the junction of the two less.
MEASURING RESISTANCE CONTAINING E. M. F. 469
239. Measuring a Resistance containing an E. M. P.
— If in one of the branches 3 4 of the Wheatstone's bridge
(Fig. 177) there be an opposing E. M. F. of e volts, Kirch-
Fig. 177.
hoffs second law tells us that equation (5) (§ 235, page
465) becomes
G^ + Ss - R?- = - e,
and equation (6) becomes
Qq + Ss -\-Bb = E - e;
the other four equations remaining as before. Using
these equations we now find that
G=: 'E'jqr - ps) - e{h{p-\-q) + q (p + r)}
^ i 9 (P + q + '^ + s) -\- (p -\- q) (r -\- s)}
+ S'(p'+»*) (9 + s) + r(P -^9)(9 + 8) — q (qr — ps)
This current is obviously the difierence of two currents,
the one the current that would exist if e were nought —
470 PRACTICAL ELECTRICITY.
that is, if there were no E. M. F. in the branch 3 4 of the
bridge — the other the current that would exist if E were
nought — that is, if the testing battery had no E. M. F.
This is expressed by saying that each E. M. F. acts inde-
pendently, a result that is universally true.
If qr =. p s,
the expression given above for G reduces to simply
pe
g{jp ^r)-\-r{p^qy
the negative sign meaning that the current through
the galvanometer is now in the opposite direction to that
shown in the figure. This current is independent of E
and of h — that is to say, if the resistances be so adjusted
that q r equals p s, no change will be made in the current
through the galvanometer hy altering the value of E, or
ofh, or of both. This leads us to a very simple test for
measuring a resistance s containing an E. M. F., and
which is : — Adjust the resistances p, q, and r until on
making and breaking the circuit containing the testing
battery, no change is produced in the galvanometer deflec-
tion. Or, the testing battery may be dispensed with
altogether, and a wire of any convenient resistance sub-
stituted for it, the E. M. F. in the branch 3 4 being the
only E. M. F. employed. In that case the resistances p,
q, and r must be adjusted until, on connecting and discon-
necting this wire, no change is produced in the galvano-
meter deflection. Then
qr
P
This latter is known as " Mance^s test " for measuring the
resistance of a conductor containing an E. M. F. such as
a battery, a long telegraph line in which an E. M. F. is
produced by atmospheric causes, or by there being a
P. D. between the ground at the two ends of the line, &c.
mange's test. 471
Although connecting and disconnecting the wire that
is used to join the points 1 and 4 produces no change in
the current passing through the galvanometer when s
equals — , the current sent through the circuit by e is
increased on connecting the auxiliary wire used to
join the points 1 and 4. Hence, this test can only be
employed when e, the E. M. F. in the branch 3 4, is not
altered by varying the cuiTent sent by this E, M. F.
through the circuit.
Examjde 120. — Prove directly the formula employed
in Mance's test for measuring the resistance of a conductor
containing an E. M. F.
From Fig 178^ which shows the distribution lify cur-
Fig. 178.
rents when the wire used to join the points 1 and 4 is
disconnected, we have
R = P-f G (1)
P(p + g)-G^= 0 (2)
R(r f s) + G^ = e o . o . . . (3)
472
PRACTICAL ELECTRICITY.
When this wire is joined, all the currents will be
altered except G. Let them now be P', Q', R', S' (Fig.
179), then
S' = Q' + G . . . . (4)
H' = P' + G . . . . (5)
F;9 + Q'^-G^= 0 (6)
R'r -\-^'s -\- Gg = e (7)
Fig. 179.
From equations (2) and (6) we have
(P-P');,= (Q'-P)? .
and from equations (3) and (7)
(R- R>= (S' -R)s .
From equations (1) and (5) it follows that
P - P' = R - R',
and from equations (1) and (4) that
Q' _ P = s' - R,
(8)
(9)
EXAMPLES.
473
therefore substituting these values in equations (8) and
(9) we have
r s
Example 121.— A battery having an E. M. F. of 3 J
volts and a resistance of 2| ohms, is employed in sending
a current through a circuit consisting of a resistance of
1,234 ohms in series with a galvanometer of 52 ohms'
Fig. 180.
resistance, shunted with a shunt of 4J ohms' resistance,
containing an opposing E. M. F of 1 volt. What is the
current flowing through the galvanometer 1
The arrangement of the circuit is shown in Fig. 180,
and if B, G, and S be the currents in amperes flowing
respectively through the battery, the galvanometer, and
the shunt, we have by Kirchhoff's first and second laws,
B = S + G,
(2i + 1,234) B + 52 G = 3i,
52 G - 4J S = 1.
474 PRACTICAL ELECTRICITY..
Eliminating B and S from these three equations, we
and
G = 0-01786.
Answer. — 0* 01 786 amperes.
Example 122. — What E. M. F. must be inserted in
the shunt in the last question so that no current shall
pass through the shunt ?
Let e be this E. M. F. in volts, then we must find the
value of e that makes S equal to nought in the following
equations : —
B = S + G,
l,236i-B + 52G = 3J,
52 G - 4J S = e.
Putting S equal to nought we have
1,288JG= 31
52 G = e,
« • , e = ^ volts.
1,288J
Answer. — 0*1413 volts.
This question may be solved differently thus : — If no
current passes through the shunt, the E. M. F. must be
equal and opposite to the P. D. that would be produced
between the terminals of the galvanometer if there were
no shunt circuit at all, and this we know, from § 115,
page 204, is equal to the E. M. F. of the battery multi-
plied by the ratio of the resistance of the galvanometer
to that of the whole of the circuit, or
^" X 3^ volts,
l,288i
the same expression that is given above for e.
EXAMPLES. 475
Example 123. — Does the presence of the shunt in
«>xample 121 increase or diminish the current that would
pass through the galvanometer if there were no shunt
circuit, and by what amount is the galvanometer current
varied ]
If there were no shunt the current through the
galvanometer would be
^i_, or 0-002717 amperes.
1,288J
We see, therefore, that the shunt in this particular
case, in consequence of the E. M. F. in it, actually in-
creases the galvanometer current by
0-01786 - 0-002717, or 16-thousandths of an ampere.
476
Specimens of Instructions for Experiments,
CITY AND GUILDS OF LONDON INSTITUTE.
CENTRAL INSTITUTION.
PHYSICAL DEPARTMENT.
To compare the amount of CHEMICAL DECOMPOSITION
produced per second by a current with the corre-
sponding DEFLECTION of a TANGENT GALVANO-
METER.
Preliminary. — The current passing through the volta-
meter and galvanometer can be varied by altering the
resistance in circuit. The value of the resistance need
not be known.
When the clip is firmly fixed on the small piece of
indiarubber tube, the gas evolved by passing a current
through the voltameter cannot escape, and so the pressure
inside becomes greater than the atmospheric pressure,
and forces the liquid up the glass tube. The rate at
which the liquid rises in the tube is a measure of the
amount of gas evolved per second. Releasing the clip
allows the gas to escape. The volume of the tube be-
tween the two marks 0 and 7 is 2*284 cubic centimetres.
Experiments. — (1.) Adjust the needle of the galva-
nometer to zero by slightly turning the instrument.
(2.) Send a current through the apparatus by pressing
the key, and open the clip so that the gas escapes. Keep
the key pressed for a few minutes, until the liquid be-
comes thoroughly saturated with gas. Now close the
INSTRUCTIONS FOR EXPERIMENTS. 477
clip, and note the interval of time it takes for the liquid
to rise from the lowest to the highest mark on the tube ;
also note the steady deflection of the galvanometer.*
(3.) Vary the current by altering the resistance in
circuit, and repeat the observation mentioned in (2).
(4.) Repeat (3) with as many diflferent strengths of
currents as possible.
(5.) Tabulate your results in a convenient form.
(6.) Draw a curve having for abscissae the quantity
of gas evolved per second, and for ordinates the tangents
of the corresponding deflections of the galvanometer.
Deductions. — Write out clearly all the inferences
which can be drawn from this experiment, assuming that
the strengths of currents are proportional to the amount
of chemical decomposition which they produce per second.
Determine the constant a of the galvanometer such
that
A = a tan. c?,
where A is the current in amperes and d the deflection it
produces, having given that
1 ampere liberates 0-1738 c.c. of mixed gas per second,
when measured at 0° 0. and 760 m.m. pressure.
State clearly the corrections which would have to be
applied in making accurate determinations of current
strength by this method.
* It is desirable to make two or three determinations with each
particular current, and take the mean.
478 PRACTICAL ELECTRICITY.
CITY AND GUILDS OF LONDON INSTITUTE.
CENTRAL INSTITUTION.
PHYSICAL DEPARTMENT.
EXPERIMENTS on SHUNTS.
Preliminary. — When the current to be measured in
a,ny circuit is too large for the galvanometer available to
measure it, only a known fraction of the current is passed
through the galvanometer, the remainder being passed
from one terminal of the galvanometer to the other
through a " hy:pass " or " shunt " circuit. As, however,
the introduction of this shunt circuit lessens the resist-
ance between the terminals of the galvanometer, and
therefore the total resistance used in the experiment, the
main current is increased. Thus it may happen that the
effect of shunting a galvanometer is to scarcely diminish
the current passing through it.
The following experiments have been devised to make
the student practically acquainted with the effect of
shunting a galvanometer, and the manner in which the
effect of a given shunt depends on the resistance in the
other parts of the circuit.
The resistance of the galvanometer circuit unshunted
is about 200 ohms.
Experiments. — (1.) Using one cell of the battery,
and with no resistance in the main circuit excepting that
of galvanometer, battery, and connecting wires, send a
current through the unshunted galvanometer and note
the deflection d produced.
(2.) Place various resistances from the highest avail-
able down to 0 in the shunt circuit, and note all the
corresponding deflections.
(3.) Tabulate your results in some convenient form.
INSTRUCTIONS FOR EXPERIMENTS. 479
(4.) Plot a curve having for abscissae the resistances
in the shunt circuit, and for ordinates the corresponding
currents passing through the galvanometer.
(5.) Join up two cells of the battery, and introduce
such a resistance into the main circuit as will give the
same deflection d as was obtained in (1) when the galva-
nometer was unshunted.
(6.) Repeat (2), (3), (4), drawing the curve on the
same sheet of paper.
(7.) Hepeat (5) and (6), using four and six cells re-
spectively.
Deductions. — Write out a clear account of the in-
ferences which you can draw from these experiments.
Also determine algebraically the general equation to, and charac-
ter of, the curves obtained in these experiments, and show how the
results obtained experimentally could be deduced from this equation.
Prove that the curves have a common asymptote, and find the limits
between which the other asymptotes lie.
480 PRACTICAL ELECTRICITY.
CITY AND GUILDS OF LONDON INSTITUTE.
CENTRAL INSTITUTION.
PHYSICAL DEPARTMENT.
Vo CALIBRATE an AMMETER by the CALORIMETRIC
METHOD.
Preliminary. — The calorimeter provided consists of
a thin copper vessel supported within an air space, and
screened from external radiation by a large water jacket.
A coil of German silver wire is inserted in the calori-
meter, and surrounds the bulb of a delicate thermometer.
This thermometer serves to show the rise of temperature
of the water and calorimeter caused by passing a current
through the wire. Another thermometer indicates the
temperature of the large water jacket in which it is im-
mersed.
Experiments. — (1.) Carefully dry and weigh the
small copper calorimeter, the approximate weight of
wliich is 24*8 grammes.
(2.) Partly fill the calorimeter with distilled water by
means of the pipette provided, and determine the weight
of the water added.
(3.) Replace the calorimeter within the water jacket
and connect the wires to the ends of the coil. Adjust
the pointer of the ammeter to zero (if necessary) by turn-
ing the small milled head at the top.
(4.) Complete the circuit, and adjust the carbon re-
sistance till a suitable deflection is obtained on the am-
meter, say 0*8, which must be maintained constant.
Keep the water well agitated by means of the stirrer,
and take " time readings " (about every half-minute) of
the temperatures of the inner and outer vessels, until the
inner thermometer has risen several degrees. Break the
circuit.
INSTRUCTIONS FOR EXPERIAIENTS. 481
(5.) Tabulate your results in a convenient form.
(6.) Plot a curve having times for abscissae and tem-
peratures of the calorimeter for ordinates.
(7.) Repeat (4), (5), (6), using successively currents
which produce deflections of about 1*1, 1-4^ 1*7, and 2-0
on the ammeter.
(8.) When all the heating observations have been
taken, break the circuit, and allow the calorimeter to
cool to nearly its initial temperature, and take time
readings of its temperature, keeping the water well
stirred all the while.
(9.) Plot a '•^.cooling curve " from the observations
obtained in (8).
(10.) Correct the heating curves obtained in (6) and
(7) by the cooling curve (9), and determine the corrected
rise of temperature in a given time (say five minutes).
(11.) Calculate the strength of current passing in
each of the above experiments from the formula
V 0-24
X rt
where A stands for the current in amperes,
„ r „ „ resistance of the coil in ohms,
which is 1-0306 at 15°-6 C.
„ W „ „ weight of the water in grammes,
J, 2« „ „ water-equivalent of the calori-
meter, thermometer, &c., which
equals 2778 grammes,
„ T „ „ corrected rise of temperature in
t seconds,
„ t „ „ time in seconds,
and compare the values so obtained with the graduations
of the ammeter.
Deductions. — State clearly how the heating curves
are corrected from the cooling curve so as to show
what would have been the true rise of temperature if no
cooling had taken place during the experiment.
P F
482 PRACTICAL ELEUTRICITT.
CITY AND GUILDS OF LONDON INSTITUTR
CENTRAL INSTITUTION.
PHYSICAL DEPARTMENT.
To CALIBRATE an AMMETER by means of a SILVER
VOLTAMETER.
Preliminary. — The voltameter consists of a platinum
dish containing a 25 per cent, solution of silver nitrate,
and in which a silver plate is immersed. An adjustable
carbon resistance is provided, by means of which the cur-
rent passing through the voltameter can be maintained
constant during each experiment, and can be varied in the
different experiments.
Experiments. — (1.) Carefully clean, dry, and weigh
the platinum dish, the approximate weight of which is 78
grammes.
(2.) Pour the solution of silver nitrate into the dish
and place it on the three brass pins provided for its re-
ception, and which are electrically connected with the
left-hand binding screw on the board. Immerse the
silver plate in the solution, and clamp it in such a posi-
tion that its edges are equally distant from the sides and
bottom of the dish.
(3.) Turn the small milled head at the top of the
ammeter so that the pointer of the ammeter comes oppo-
site the zero on the scale, if not there already. Place the
copper connecting wire in the mercury cups marked A
and 0 (which cuts out the voltameter), and adjust the
carbon resistance until a convenient current flows round
the ammeter. Remove the connecting wire.
(4.) Quickly insert the connecting wire in the mer-
cury cups marked A and B, carefully noting the instant
at which the circuit was completed. Allow the current
INSTRUCTIONS FOR EXPERIMENTS. 483
to pass for a convenient time (10 to 30 minutes, accord-
ing to the strength of current used), and keep the current
constant by the adjustable resistance. Note the tem-
perature of the room during the experiment, and, at the
end of the interval decided on, quickly break the circuit.
(5.) Empty the solution .from the dish into its bottle
and carefully wash the deposited silver with distilled
water. Then fill the dish with distilled water and allow
it to stand 10 to 15 minutes. Again wash with water,
alcohol, and ether, dry over the spirit-lamp, and cool in
the desiccator.
(6.) Carefully determine the increase of weight due
to the silver deposited on the dish.
(7.) Calculate, the strength of current used in the
experiment, assuming that one ampere deposits 1 '11815
milligrammes of silver per second.
(8.) Kepeat the experiment with several different
strengths of current.
(9.) Tabulate your results in some convenient form
and write them with your name on the card, on which
you will find recorded the results of previous experiments.
INDEX.
ABSOLUTE Calibration, Galva-
nometers with Invariable,
57
Calibration of Galvanometers,
30, 396—400
Calibration of a Galvanometer,
Meaning of, 22
Calibration of Potential Differ-
ence Galvanometers, 127,
408—415
Calibration, Portable Galvano-
meter with Approximate,
69—71
Electrometer, 93
Measurement of Capacity, 327
Units, 141
Accumulating Influence Machines,
361 ; Holtz's, 367 ; JSTichol-
son's, 366 ; Thomson's, 364 ;
Varley's, 367; Voss, 367;
Wimshurst, 367. (Soe also
Influence Machiaes.)
Accumulator, Measuring Resistance
of, 206
Accumulators, Small Internal Re-
sistance of, 206, 261
Accuracy of Graduation, Testing
Ammeters for, 395
of Graduation, Testing Volt-
meters for, 408
of Readings with Tangent and
Degree Scales Compared,40
Acid, Dilute Sulphm-ic, Effect of
Electrolysis of, 15
Sulphuric, Voltameter. (See
Sulphuric Acid Volta-
meter.)
Action, Inductive, 87
of the Electrophorus, 356—361
Adjustment for Sensibility in Mag-
nifying Spring Ammeters
and Voltmeters, 389
of Coil of Tangent Galvano-
meter, 46
Advantage of Poggendorff's Method
of Comparing Electro-
motive Forces, 236
Advantages of Cardew's Voltmeter,
426
of Cunynghame's Ammeter and
Voltmeter, 385
of Electro-Magnetic Control
Meters, 394
Advantages of Gravity Control
Meters, 391
of Magnifying Spring Ammeter
and Voltmeter, 390
of Permanent Magnet Meters, 78
- — of Shielded, Dead -Beat, Di-
rect - Reading Galvanome-
ters, 78
of Siemens' Electro-Dynamo-
meter, 380
of Thomson's Large Current
Galvanometer, 53
Relative, of Voltameters and
Galvanometers, 20
Air Condenser, Standard, 334
Specific Inductive Capacity of,
at Different Pressures, 310
Alternating Currents, Definition,
and Measurement of, 198,
381
Potential Difference Increases
Practical Resistance of
Voltmeter, 427
Potential Difference, Measur-
ing, 426
Aluminium, Resistance of, for Given
Length and Diameter, or
for Given Length and
Weight, 157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Amalgam, Definition of, 218
Amalgamate, How to, 218
Ammeter, Advantages and Disad-
vantages of Cunynghame's,
38o
Advantages and Disadvantage
of Permanent Magnet, 78,
376
Advantages and Disadvantage
of Magnifying Spring, 390
Adjustment for Sensibility in
Magnifying Spring, 389
Calibrating Commutator, 432
Commutator,Description of,427
Commutator, Safety Arrange-
ment with, 432
Cunynghame's Description of,
382
Graduation of Cunynghame's,
385
for Large Currents, Use of
Commutator in CaUbrating,
428-^31
486
PRACTICAL ELECTRICITY.
Ammeter, Indication of Direction
of Current in Magnifying
Spring, 389
Magnifving Spring, Description
of.'sse
>— Permanent Magnet, Descrip-
tion of, 76
Permanent Magnet, Propor-
tional, 71
Eatio of Sensibilities of Com-
mutator in Parallel, and in
Series, 431
Ammeters, 76— 79, 382, 386. (See also
Meters. )
— Calibrating', by tbe Silver De-
posit Method, 395-400
Testing-, 394
Testing, for Accuracy of Gra-
duation, 395—400
Testing, for Error on Reversing
Current, 402
— — Testing, for Error Produced
by External Magnetic Dis
turbance, 403—407
'— Testing, for Permanent Altera
tion o! Sensibility, 407
Testing, for Residual Mag-
netism, 400
'— with Magnifying Gearing, 386,
(See also Dynamometer,
Galvanometer. )
Amount of a Body's Electrification
109
of Electricity, Dependence of
Potential of Conductor
Partly on, 119
-^of Heat produced per Minute
by Given Current Flowing
through Given Resistance,
1£9
— of Heat produced per Minute,
Measurement of Currents
by, 197
Ampere, Definition of the, 11
Amperes, Values in, of Deflections
of Tangent Galvanometer,
Controlled only by Earth's
Magnetism, 55
Angles, Finding, from their Tan-
gents by means of Squared
Paper, 66
— Finding Tangents from, by
means of Squared Paper,
57
Angular Deflection of a Mirror,
Connection between, and
Motion of Image on Plane
Scale, 107
•—— Deflection Proportional to Cur-
rent, Construction of Gal-
vanometers with, 71—73
Motion of Reflected Ray is
Twice Angular Motion of
Mirror, 106
Antimony, Change of Resistance of,
with Temperature, 160
Resistance of, for Given Length
and Diameter, and for
given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Incb,
154
Apparatus for Measuring Variation
of Current and Potential
Ditference at Battery Ter-
minals with Variation of
External Resistance, 205
Static Electric, Necessary En-
closure of, in Metallic Case,
108
Apparent Increase of Resistance
in a Galvanometer Due to
Damping, 349
Approximate Absolute Calibration,
Portable Galvanometer
with, 69—71
Arc, Electric, Description of, 188,
454
Electric, Measuring lUumiuat-
• ing Power of, in Any Plane,
457
Light, How to Overcome Differ-
ence in Colour between it
and Candle when Measur-
ing. 457
Light, Measuring the Efficiency
of, 455
Potential Difference Required
to Maintain an Electric,
betwfien Two Carbons, 371
Area, Sectional, Variation of Re-
sistance with, 146
Arms of Wheatstone's Bridge, Defi-
nition of, 172
Arrangement for Shunting Battery
while Charging Condenser
only, 343
of Cells, giving Maximum ITse-
f ul Power to Conductor of
Fixed Resistance, 450
'■ of Given Number of Cells to
produce Maximum Current
through Given External
Resistance, 243
Arrangements of Cells, 239—253
Astatic Combination of Magnets,
283
Galvanometer, Advantage of
Putting Mirror Outside
Coils, 284
Galvanometer, Simple Method
of Damping, 284, 300
Galvanometer, Mather's, 299
INDEX.
487
Astatic Galvanometer, Mudford's,
105
Galvanometer, Thomson's, 283
Galvanometer, Thomson's
Modified, 284
Attaching Leyden Jars to Collect-
ing Combs of Electrical
Machines, 370
Attracting Force, Potential Differ-
ence and Distance between
Two Parallel Plane Con-
ductors, 87
Axis, Magnetic, of a Needle, Defiui-
tion of, 37
B
■HALANCE, Wheatstone's, 166—
177. (See also Wheatstone's
Bridge.)
Ballistic Galvanometer, 292
Batteries, 209 ; Bunsen's, 219 ; Cal-
laud, 213; Dauiell's, 211;
Gravity, 212 ; Grove's, 218 ;
Leclanch6, 220 ; Lockwood,
213; Meidinger, 212; Min-
otto's, 211 ; Potash Bichro-
mate, 222; Secondary, 206,
261. (See also Cells.)
— Compaiison of Electromotive
Forces of, by Observing
tbeir Joint and Opposed
Currents, 232
Compirison of Electromotive
Forces of, by Observing
Resistance through which
they send Equal Currents,
231
Comparison of Electromotive
Forces of. Condenser Me-
thod of, 311
Comparison of Electromotive
Forces of, P<iggendorif's
Method of, 241
Local Action in, 217
Measuring Eesistances of, 205,
225, 342
Polarisation in, 216
■ Figures of, 239
Symbolical Eepresentation of,
173, 240
Battery and G alvanometer in Wheat-
stone's Bridge, Best Ar-
rangement of, 172, 467
Arrangement for Shunting
while Charging Condenser
only, 343
of Leyden Jars, 317
of Simple Voltaic Elements
for Cliarging Electrometer
Needle, 373
B. A. Unit of Resistance, 141
B. A. Units and Legal Ohms, Equa-
tion Connecting, 142
Bell Telephone, Description of,
336
Bertsch's Rotatory Electrophorus,
361
Best Arrangement of Battery and
Galvanometer in Wheat-
stone's Bridge, 172, 467
— — Deflection to use with Tangent
Galvanometer, 41
Resistance for Coils of Wheat
stone's Bridge, 170
Resistance for Differential Gal-
vanometer, 436
Resistance for Galvanometer in
Simple Circuit, 435
Resistance for Galvanometer in
Wheatstone's Bridge, 171,
466
Resistance to Give to a Galvano-
meter, 435
Bichromate of Potash Cell, Descrip-
tion of, 222
of Potash Cell, Chemical Action
in, 223
of Potash Cell, Compositi .n of
Liquid for, 222
of Potash Cell, Electromotive
Force of, 223
Bismuth, Change of Resistance of,
with Temperature, 160
Electric and Heat Conductivi-
ties of, Compared, 159
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
: Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Bobbin of Tangent Galvanometer,
Proportions of Channel in,
when Tangent Law is most
Accurately Fulfilled, 51
Variation of Magnetic Effect of,
with Current and Resist-
ance, 418
Variation of the Sensibility of
a Tangent Galvanometer,
with Diameter of, 48—51
Bridge, Wheatstone's, 166—177
Wheatstone's, Best Arrange-
ment of Battery and Gal-
vanometer with, 172, 467
Wheatstone's, Best Resistance
of Galvanometer for, 171,
466
Wheatstone's, Best Resistance
of Coils for, 171
Wheatstone's, British Associa-
tion Form of, 168
488
PRACTICAL ELECTRICITY.
Bridge, Wheatstone's, Commercial
Form of, 172
Wheatstone's, Conditions Af-
fecting Sensibility of, 171
Wheatstone's, Key for, 174
- — Wheatstone's, Meaning of De-
flection of Galvanometer
of, 176
- — Wheatstone's, Metre Form of,
168
— =- Wheatstone's, Superiority of,
over Differential Galvano-
meter, 171
Wheatstone's, Use of Shunt
with, 176
British Association Absolute Units,
141
Association Bridge, 168
Association Unit of Resistance,
141
Brush Discharge, 369
Bunsen's Cell, Description of, 219
Cell, Carbon for, 220
Cell, Chemical Action in, 219
Cell, Electromotive Force of,
220
Butt Joint, 79
CABLE, Capacity of a Submarine,
309
Sealing up One End of, when
Testing, 268
Calibrating Ammeters by the Silver
Deposit Method, 395-^:00
Ammeters for Large Currents,
Use of Commutator for, 428
Commutator Ammeter, 432
Commutator Voltmeter, 433
Galvanometer by Direct Com-
parison with Tangent Gal-
vanometer, 58
Galvanometer by Emi^loying
Known Resistances and
Cell of Constant E. M. F.,
238
Galvanometer by Employing
Known Resistances and
Fixed Potential Differ-
ence, 164
Galvanometer by Sine Method,
64
—— Galvanometer, by Sine Method,
Higher Parts of Scale of, 65
— Galvanometer by Sine Method
with Constant Current, 67
— — Gkilvanometer, Relatively or
Absolutely, Meaning of, 22
— Galvanometer, Relatively or
Absolutely, Mode of, 27—30
* — Gold-Leaf Electroscope, 354
Calibrating Voltmeter by Compari-
son with Standard Cell,
410-415
Voltmeter by Poggendorflfs
Method, 413
Voltmeter with a Known Cur-
rent and Resistance, 408
Cahbra'ion, Absolute, of Potential
Difference Galvanometer,
127, 408-415
of Galvanometer Unaffected by
Change in Strength of Poles
of Needle, 23
Galvanometers with Invariable
Absolute, 57
Portable Galvanometer with
Approximate Absolute, 69
Callaud Cell, Description of, 213
Candle, Description of Standard, 452
Candles instead of Standard Can-
dles for Rough Experi-
ments, 452
Capacities, Comparison of, 319
Statical Method of Comparing,
330
Capacity, Absolute Measurement
of, 327
Charge in Terms of, 303
Construction of Condensers of
Very Large, 317
- — Definition of, 300
Measuring Specifi.c Inductive,
332
of Condenser is Constant, 302
of Condenser, Variation of, with
Area of its Coatings, 303
of Condenser, Variatioa of,
with Distance betwe n its
Coatings, 303
of Condenser, with Plane
Parallel Plates, varies in-
versely as Distance be-
tween its Coatings, 307
of Cylindrical Condenser, 303
of Sphere in Space, 339
of Spherical Coudensf-r, 338
of Submarine Cable, 309
of Collectors of Influence Ma-
chines, Increasing the, 370
of Two Bodies Constant while
their Relative Positions are
Constant, 338
Unit of, 307
Specific Inductive, 309
Carbonic Dioxide, Specific Induc-
tive Capacity of, 310
Carbonised Cloth, Preparation of,
for Varley's Resistances, 397
Carbons for Bunsen's Cells, Mode
of Making, 220
Cardew's Voltmeter, Description of
the Latest Form of, 423
INDEX
489
Cardew's Voltmeter, Advantages of,
426
Voltmeter Arranged for
Measuriug Large Potential
DiffereiiC3s, 425
Voltmeter, Coustniction of
Rods in, to Prevent Change
of Length with Tempera-
ture, 426
Voltmeter, Diameter of Wire
used in, 423
Voltmeter, Disadvantages of
427
Voltmeter, Length of Wire
used in the Latest Form
of, 423
Voltmeter, No Heating Error
in, 426
Voltmeter, Small Self-induc-
tion in, 427
Cell, Bunsen's, 219
Callaud, 213
Danieil's, 210
Fleming's Standard Danieil's,
412
Gravity Danieil's, 212
Grove's, 218
Leclanch^, 220
Latimer Clark's, 410
Lockwood's, 213
• Meidinger's, 212
Minotto's, 211
Potash Bichromate, 222
Standard Danieil's, 411
Chemical Action in a Bunsen's,
220
Chemical Action in a Danieil's,
214
Chemical Action in a Grove's,
219
Chemical Action in a Leclanch«5,
221
Chemical Action in a Potash
Bichromate, 223
Carbon for Bunsen's, 220
Composition of Liquid for Pot-
ash Bichromate, 222
Constancy of E. M. F. of a
Danieil's, 216
Constancy of E.M. F. of a
Latimer Clark's, 411
E. M. F. of a Bunsen's, 220
E. M. P. of a Danieil's, 211
E. M. F. of a Standard Danieil's,
412
E. M. F. of a Grove's, 218
E. M. F. of a Latimer Clark's,
411
E. M. F. of a Leclanchd, 222
E. M. F. of, Independent of
Size and Shape, 211, 236
— — E. M. F., Temperature Varia-
tion of, in Latimer Clark's,
411
Cell, E. M. Fs. of. Comparison of,
231, 232, 234, 341
Local Action in, 217
How- to prevent Local Action
in a Danieil's, 217
Polarisation in a Danieil's,
216
Resistance of a Danieil's, 211
Resistance of a Grove's, 218
Resistance of. Measuring, 205,
225, 342
Cells, Arrangement of, 239
Arrangement of a Given Num-
ber of, to produce Maxi-
mum Current through a
Given External Resistance,
243
Arrangement of for Giving
Maximum Useful Power
to Conductor with Fixed
Resistance, 450
Galvanic, 209
in Parallel, E. M. F. of, 241
Figure of, 239
Symbolical Representation of,
240
in Series, E. M. F. of, 241
in Series, Figure of, 239
in Series, Symbolical Repre-
sentation of, 240
Partly in Parallel and Partly
in Series, E. M. F. of, 241
Partly in Parallel and Partly
in Series, Figure of, 239
Partly in Parallel and Partly
in Series, Symbolical Repre-
sentation of, 240
Standard, 410
Change in Strength of Poles of
Needle of Galvanometer,
Calibration Unaffected by,
23
of Resistance with Tempera-
ture, Results of Matthies-
sen's Exijeriments on, 160
Charge. (See Quantity.)
and Discharge Key, Descrip-
tion of, 320, 343
and Discbarge Key, Various
Modes of attaching to Con-
denser, Battery, and Gal-
vanometer, 320—322
Rate of Loss of, Depends on
Dielectric Alone, 346
Electric, Meaning of, 109
Galvanometric Method of Mea-
suring Resistance by Loss
of, 348
in Condenser in Terms of Car
pacity, 308
490
PRACTICAL ELECTRICITY.
Cliarge, Measuring Resistance by
Rate of Loss of, 343
Remaining on Two Bodies after
Contact, 115, 351
Charged Body cannot Exist Alone,
339
Charges induced in Hollow Con-
ductor by placing a Charged
Body inside it, 113
—— on Two Conductors Enclosed
by a Third, 110
— on Two Bodies not Measured
by the Potential Differ-
ence, 85
Chemical Action in the Bunseu's
Cell, 220
Action in the Daniell's Cell, 214
Action in the Grove's Cell, 219
Action in the Leclanch^ Cell,
221
Action in the Potash Bichro-
mate Cell, 223
Property of a Current, Uses of, 4
Property of a Current, Why
Used to Measure Strength
of Current, 9
Circuit, Law Connecting Currents
in a Closed, 464
Wires Joined in Parallel, 136
Circuits in Pai-allel, Independence
of Currents in, 260
Clark's, Latimer, Ditferentifil Gal-
vanometer, 150
Latimer, Cell, 410
Latimer, Cell, Constancy of
E.M.F. of, 411
Latimer, Cell, E. M. F. of,
411
Latimer, Cell, Polarisation of,
411
Latimer, Cell, Temperature
Variation of E. M. F. of,
411
Closed Circuit, Law Connecting
Currents in, 464
Conductor, Density Nought on
Inner Surface of, 118
Conductor, Distribution of
Density in. Altered by In-
sertion of Metal Rod, 119
Conductor, Potential Inside,
98
Cloth, Preparation of Carbonised,
for Varley's Resistances,
397
Coating Insulating Stems witli
Paraffin Wax or Shell-lac
Varnish, 267
— — of a Condenser, Every Chained
Body forms One, 338
Coatings of a Condenser, Definition
of, 302
Coil of Tangent Galvanometer, Ad-
justment of, 46
Coils, Resistance, Construction and
Use of, 28, 145
Resistance, Construction of
Standard, 162
Resistance, Materials Used in
Winding, 159
Resistance, Germnu Silver, 160
Resistance, Iron, 162
■ Resistance, Platinoid, 160
Resistance, Platinum- Silver, 160
Resistance, Mode of Winding,
163
Resistance, Ordinary, Cannot
be Used with Strong Cur-
rents, 192
Resistance, of Magnifying
Spring Voltmeters, Best
Law of Gauge of Wire for,
421
Resistance, Temperature Va-
riation of, 153
Proportional, of Wheatstone's
Briflge, 172
Rate of Production of Heat in
Galvanometer, 419
Collecting Combs of Wimshurst In-
fluence Machine, 369
Collectors of Influence Machines,
Attaching Leyden jars to,
370
— — of Influence Machines, Increas-
ing Capacity of, 370
Combination, Astatic, 283
Combined Resistance, 178
Commercial Form of Wheatstone's
Bridge, 172
Instrumentsfor Measuring Cur-
rent, 79, 376
Commutator Ammeter and Volt-
meter, 427
Ammeter, Calibrating, 432
Ammeter, Ratio of Sensibili-
ties of, in Parallel and in
Series, 431
Ammeter, Safety Arrangement
with, 432
Use of, in Cdlibrating Amme-
ters for Large Currents, 428
Use of, in Calibrating Voltme-
ters, for large Potential
Differences, 428
Voltmeter, Calibrating a, 432
Comparing Capacities, Galvanome-
tric Method of, 319
Capacities, Statical Method of,
330
Electromotive Forces of Bat-
teries by Observing their
Joint and Opposed Cur-
rents, 232
INDEX.
491
Comparing Electromotive Forces of
Batteries by Observing the
Resistances through which
they send Equal Currents,
231
Electromotive Forces, Conden-
ser Method of, 341
Electromotive Forces, Poggen-
dorff's Method of, 234
Quantities of Electricity, Fun-
damental Statical Method
of, 111
Quantities of Electricity, Gal-
vanometric Method of, 299
Resistances, Equality of Cur-
rent Method of, 136
Resistances, Potential Differ-
ence Method of, 140
Resistances, Simple Substitu-
tion Method of, 138
Resistances, Use of Differen-
tial Galvanometer for, 148
Resistances, Use of Wheat-
stone's Bridge for, 97
Comparison of Difference of Poten-
tial with Difference of
Level in Liquids, 86
of Difference of Potential -with
Difference of Pressure in
Gases, 86
of Electric and Heat Conduc-
tivities, 158
of Measurement of Potential
with Measurement of Tem-
perature, 85
of Resistance per Cubic Centime-
tre, and per Cubic Inch, 348
of Static and Current Methods
of Measuring Potential Dif-
ferences, 125
of Use of Liquid and Wire Re-
sistances, 194
Comi)onent, Horizontal, of the
Earth's Magnetic Force,
Definition of, note, 55
Composition of Liquid for Potash
Bichromate Cell, 222
Compound Interest Law of Electio-
phoric Action, 366
Interest Law of Electrophoiic
Action, when firstlUsed, 366
Interest Law of Influence Ma-
chines, 364
Condenser, Arrangement for Shunt-
ing Battery only wiiile
Charging, 343
Capacity of, 302
Capacity of Cylindrical, 308
Capacity of Spherical, 338
Coatings of, 302
Constancy of Capacity of, 302
Definition of, 301
Condenser, Every Charged Body
forms One Coating of a, 3^
Method of Ccmparing E.M.Fs.,
341
Method of Measuring Resist-
ance of a Current Genera-
tor, 342
Standard Air, 334
Variation of Capacity of, with
Area of Coatings, 303
Variation of Capacity of, with
Distance between Coat-
ings, 303
with Plane Parallel Plates, Ca-
pacity of. Varies Inversely
as Distance between Coat-
ings, 307
Condensers for Large Potential Dif-
ferences, Construction of,
313
for use with Frictional and In-
fluence Machines, 313
not Stores of Electricity, 322
of Very Large Capacity, Con-
struction of, 317
Stores of Electric Energy, 322
Condensing Electroscope, 352
Conditions affecting Sensibility of
Wheatstone's Bridge, 171
General, for Sine Law to be
True, 62
General, for Tangent Law to be
True, 43
for Sine Law being Fulfilled?
in a Galvanometer, 62
for Tangent Law being Fulfilled
in a Galvanometer, 43
of an Experiment, Necessity for
Changing only One at a
Time, 146
to be Fulfilled in Making Tan-
gent Galvanometer, 36
to be Fulfilled in Making Very
Sensitive Galvanometer,281
Conduction and Induction, Distinc-
tion between, 97
Definition of, 97
of Heat, no^, 195
Conductivities, Comparison of Elec-
tric and Heat, 158
Conductivity, 9
Exact Definition of, 155
Electric, Dimiuishing More
Rapidly than Heat, 159
Conductor, Closed, Density Nought
on Inner Surface of, 118
Closed, Distribution of Density
in, Altered by Insertion of
Metal Rod, 119
Closed, Hollow, No Force in-
side, due to Exterior Elec-
trification, 99
492
PRACTICAL ELECTRICITY.
Conductor, Conical, Electric Density
Great at Pointed End of,
118
Dependence of Potential of, on
Amount of Electricity on
it, 119
Dependence of Potential of, on
Position, 119
Dependence of Potential of, on
Shape, 119
Electric, Heat evolved in, 3, 199
Electricity at Rest resides only
on Surface of, 119
of Fixed Resistimce, Arrange-
ment of Cells giving Maxi-
mum Useful Povrer to, 450
Potential inside a Closed, 98
Potential of, compared with
Pressiire of Gas, 121
Uniform Potential on a, 86
• Ways in which Potential of,
can be Varied, 121
Conductors, 9
• Charges on Two, Enclosed hy a
Thu-d, 110
of Different Potential, Induc-
tive Action between, 87
Conical Conductor, Electric Density
Great at Pointed End of,
118
Connection between Angular Motion
of Reflected Ray and of
Mirror, 106
between Motion of Image on
a Plane Scale and Angular
Deflection of Mirror, 107
between Poles of Magnet and
Direction of Current cir-
culating round Magnet, 17
Constancy of Capacity of Condenser,
302
of Capacity of Two Bodies while
their Relative Positions
remain Constant, 338
of E.M.P. of Daniell's Cell,
216
of E. M. F. of Latimer Clark's
Cell, 411
of Rate of Production of Heat
in a Wire by Constant Cur-
rent, 197
Constant Current, Calibration by
Sine Method with, &7
of a Galvanometer, 278
■ Total, Current Shunts, 257
Constructing Voltameters, Objec-
tions to usual Mode of, 17
Contact Potential Difference, 351
Controlling Field, Galvanometer
having Uniform, in which
Deflection Varies as Cur-
rent, 72
Controlling Force caused by Powei
ful Permanent Magnet,
Galvanometers having, 73
Convection of Heat, note, 195
Cooling Correction of Observed Rise
of Temperature Curve, 196
Copper, Change of Resistance of,
with Temperature, 160
Electric and Heat Conductivi-
ties of. Compared, 159
Resistance of, for Given Length
and Diameter, and fo*"
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Voltameter, Description of, 6, 11
Voltameter, Direction of Cur-
rent in, 15
Voltameter, Precautions in
Using, note, 11
Voltameter, Weight of Copper
deposited on Plate of, per
second, by one Ampei'e, 11
Cores, Soft Iron, used in Galvano-
meters, 73
Correcting Results of Experiments
by Drawing Curves, 34
Correction, Cooling, of Observed
Rise of Temperature
Curve, 196
Correction for Damping, 296
Corrugating Sides of Ebonite Pil-
lars, 272
Coulomb, Definition of the, 289
Couple, Definition of, note, 283
Definition of Moment of a,
note, 283
Crompton and Kapp's Electro-Mag-
netic Control Meters, 392
and Kapp's Electro-Magnetic
Control Meters, Advant-
ages and Disadvantages of,
394
Cunynghame's Ammeter and Volt-
meter, 382
Ammeter and Voltmeter, Ad-
vantages and Disadvant-
ages of, 385
Ammeter and Voltmeter,
Graduation of, 385
Current, Alternating, Definition of,
198
Alternating, Measurement of,
198, 381
Amount of Heat Generated by
Electric, 192
Amoiint of Heat produced per
Minute by given, in given
Resistance, 199
Arrangement of given Numbei
INDEX.
493
of Cells to^produce Maxi-
mum, through given Ex-
ternal Eesistance, 243
Current and Eesistance, Variation of
Magnetic Effect of Bobbin
with, 418
and Static Methods of Measu-
ring Potential Diiierences
Compared, 125
Calibration by Sine Method
with Constant, 67
Commercial Instruments for
Measuring, 79, 376
Connection between Direction
of, and Poles of Magnet
producer], 17
Constancy of Rate of Produc-
tion of Heat in a given
Coil by Constant, 197
Definition of Direction of, 14
■ Developing Maximum Useful
Power in Generator with
Fixed E.M.P. and Eesist-
ance, 448
Direction of, in Acid, Copper,
and Zinc Voltameters, 15
Du'ection of, round Magnet,
and Poles produced, 17
Electric, Compare*? with Cur-
rent of Water /", 80
Electric, Heat is Evolved by, 3
Electric, Liquid is Decomposed
by, 3
Electric, Magnet is Deflected
by, 3
Electric, Properties of, 3
Electric, What is Meant by, 2
Electric, When said to Flow in
a Conductor, 3
Flowing Lu Flat Coil, Direction
of Magnetic Force pro-
duced by, 43
Generator, Definition of Effi-
ciency of, 451
Generator, Measurement of
E.M. F. of, 224, 231, 23 i, 341
Generator, Work doue by a, 202
Generators, 208. (See also Cell
and Batteries.)
Increase of Total, by Shunting,
183
Indication of Direction of, in
Magnifying Spring Amme-
ter and Voltmeter, 389
Measuring Alternating, 198
Measuring, by Eate of Produc-
tion of Heat, 197
Measuring Strength of, 4, 8
Measuring with Siemens' Dy-
namometer, 379
Measuring Eesistance during
Passage of Strong, 187
Current of Water in Pipe Compared
with Electric Ciurrent, 80
Properties of, 3
Proportional to Tangent of
Angle in Tangent Galva-
nometers, 43
Eatio of, to Potential Differ-
ence Constant for Given
Conductor, 130
Eesistance Coils Heated by
Strong, 192
Ee versing, without Altering ita
Value, 47
Strength, Why Measured Fun-
damentally by ChemicaJ
Property, 10
Testing Ammeters for EiTor on
Eeversivig the, 402
that Develops Maximum Use-
ful Power, 448
through the Galvanometer of
Wheatstone's Bridge, 435
Unit of, 11
Variation of, with Variation of
Potential Difference at
Battery Terminals, 204
Variation of, produced in Total,
by Shunting Part of Cir-
cuit, 253
What is Meant by, 2
Currents in Closed Circuit, Law Con-
necting, 464
in Network, 462
in Various Circuits in Parallel,
Condition of Independence
of, 260
Several, Meeting at a Point, 464
Thomson's Galvanometer for
Large, 53
Curve, Cooling Correction of Ob-
served Rise of Tempera-
ture, 196
Definition of Elastic, 34
Finding the Maximum for an
Expression by means of, 244
Interpolation of Eesults by
means of, 34
Law connecting Two Sets of
Facts determined by means
of, 35
Curves, Drawing,on Squared Paper,
31
Drawing, to Correct Eesults of
Experiments, 34
on Squared Paper, Meaning of
Apparent Inaccuracies in,
33
Value of, for Graphically Ee-
cording Eesults of Experi-
ments, 33
Cylindrical Condenser, Capacity of,
308
494
PRACTICAL ELECTRICITY.
D
T)AMPING, 291
-*-^ Apparent Increase in Re-
sistance of a Galvanometer
due to, 349
Correction for, 296
Definition of, 284
Daniell's Cell, Description of, 210
Cell, Chemical Action in, 214
Cell, Constancy of E. M. F. in,
216
Cell,E.M.F. of, 211
Cell, E. M. F. of Standard, 411
• Cell, Gravity, 212
Cell, Fleming's Standard, 412
Cell, How to Prevent Local
Action in, 217
Cell, Polarisation in, 216
Cell, Resistance of, 211
Cell, Standard, 411
Dead-Beat, Shielded, Direct-Read-
ing Galvanometers, Ad-
vantages of, 78
Decrement, Determination of Log-
arithmic, when Damping
is Very Slight, 297
Logarithmic, 296
Definition of Alternating Current,
198
of the Ampere, 11
of Brush Discharge, 369
of Capacity, 300
of Capacity of Condenser, 302
of Condenser, 301
of Conductivity, 155
of Contact Potential Difference,
351
of the Coulomb, 289
of Couple, 283
of Difference of Potentials, 80
of Damping, 284
of Dielectric, 311
of Direction of Current, 14
of Efficiency of Current Gene-
rator, 451
of Efficiency of Electric Light,
452
of Elastic Curve, 34
of Electric Density, 117
of Electromotive Force, 202
of the Farad, 307
of Galvanometer, note, 21
of Galvanoscope, note, 21
of Glow Discharge, note, 369
of Hermetically Sealing, note, 20
of Horizontal Component of
Earth's Magnetic Force,
note, 55
of Hypotenuse, note, 38
of Inductive Action, 87
of the JouIr, 461
Definition of Lines of Force, 43
of Logarithmic Decrement, 296
of Magnetic Axis of a Needle,
37
of Magnetic Saturation, 388
of Moment of Couple, note, 283
of Moment of Inertia, 78
of North-seeking End of Mag-
net, 16
of the Ohm, 140
of Parallax, note, 28
of Periodic Time of Vibration,
291
of Plane of Magnetic Meridian,
note, 45
of Potential Difference, 80
of Power, 441
of Quantity of Electricity, 109
of Residual Magnetism, 385
of Retardation, 331
of the Saturation of Liquid, 411
of Short-Circuited, 217
of Sine, note, 38
of Solenoid, note, 387
of Specific Inductive Capacity,
309
of Striking Distance, note, 371
of Super-saturation, note, 411
of Tangent, note, 37
of the Volt, Legal, 141
of the Volt, Provisional, 89
of Uniform Magnetic Field, 36
of Water Equivalent, 198
of the Watt, 442
Definitions of Conduction and In-
duction, 97
Deflecting Field, Magnetic, 73
Deflection, Angular, of Mirror, Con-
nection between, and Mo-
tion of Image on Plane
Scale, 107
Best, to use with Tangent Gal-
vanometer, 41
with Galvanometer of Wheat-
stone's Bridge, Meaning of,
176
Proportional to Current, Con-
struction of Galvanometers
with, 71
Deflections of Tangent Galvanometer
Controlled Only by Earth's
Magnetism, Values in Am-
peres of, 84
Degree andTangent Scales, Accuracy
of Readings Compared, 40
Delicate Galvanometers, 281. (See
also Galvanometer.)
Galvanometers, Importance of
being Well Insulated, 286
Density, Distribution of, in Closed
(Conductor Altered by In-
sertion of Metal Rod, lli)
INDEX.
495
Density Electric, Definition of, 117
Electric, Great at Pointed End
of a Conical Conductor, 118
• Electi-ic, Greater near Edges of
Plat Sheet of Metal, 118
Electric, Measuring, by means
of Proof Plane, 117
Electric, Nought on Inner Sur-
face of Closed Conductor,
118
Electric, Potential, and Quan-
tity, Examples showing
Difference between, 121
Dependence of Rate of .Loss of
Charge on Dielectric Only,
346
Deprez, E. M. F, used by, in Trans-
mitting Power Thirty-
seven Miles, 452
Detector, 68
Determination of Logarithmic De-
crement when Damping is
very Slight, 297
Diameter of Bobbin, Variation of
Sensibility of Galvanome-
ter with, 48
Dielectric, Deiinition of, 311
Only, Dependence of Rate of
Loss of Charge on, 347
Difference between Saturation and
Super-saturation, note, 411
— — in Colour between Candle and
Arc Light, How to Over-
come, in Measuring Arc
Light, 457
of Potential, Adjusting Balls
of Electrical Machine to
produce Given Maximum,
372
——of Potential, Alternating, In-
creases Practical Kesist-
ance of Voltmeters, 427
of Potential, Alternating, Mea-
suring, 426
of Potential at Battery Termi-
nals, Variation of, with
Change of Current, 204
of Potential between Two
Conductors not Measuring
Difference in their Electric
Charges, 85
of Potential between Two
Plane Conductors, Formula
connecting, with Distance
and Attraction between
them, 87
— of Potential between Two
Points in a Uniform Wire
Conveying Current Pro-
portional to Distance be-
tween them, 83
of Potential, Charges on Two
Conductors Vary as, while
their Relative Positions re-
main Constant, 110
Difference of Potential Compared
with Difference of Level in
Liquids, 86
of Potential Compared with
Difference of Pressure in
of Potential Compared with
Difference of Pressui-e of
"Water Flowing in a Pipe,
81
of Potential, Contact, 351
of Potential, Definition of, 80
of Potential Galvanometer Ab-
solutely Calibrated, 127,
408, 415
of Potential Galvanometer,
Long Fine "Wire Used in,
127
of Potential Galvanometer,
When it may be Employed,
127
of Potential, Increasing a, in
Known Ratio, 354
of Potential, Large, 351
of Potential, Measuring, by
Weighing, 88
of Potential Method of Com-
paring Resistances, 140
of Potential, Ratio of, to Cur-
rent, Constant for Given
Conductor, 130
of Potential, Ratio of, to Cur-
rent is Resistance, 130
of Potential Required to Main-
tain Electric Arc between
Two Carbons, note, 371
of Potential Required to Pro-
duce Spark between Point
and Plate, 371
of Potential Required to Pro-
duce Spark between Two
Metallic Balls, 370
of Potential, Static and Cur-
rent Methods of Measur-
ing, Compared, 125
of Potential, Sub-dividing into
Known Fractious, 278
of Potential, Unit of, 89, 141
of Potential, Variation of, with
Resistance of Given Volt-
meter to Produce Given
Deflection, 419
Differences between Electric Poten-
tial and Pressure of Water
Flowing in a Pipe, 83
Differential Galvanometer, Best Re-
sistance for, 436
Galvanometer, Construction of,
149
496
PRACTICAL ELECTRICITY.
Differential Galvanometer, Latimer
Clark's, 150
Galvanometer, Mode of Ad-
justing, 150
• Galvanometer, Principle of, 148
Galvanometer, Superiority of
Wheatstone's Bridge over,
171
Galvanometer, Use of Shunts
with, 183
Dilute Sulphuric Acid, Effect of
Electrolysis of, 15
Diminution of Resistance of In-
sulators with Increase of
Temperature, 271
Direct Comparison with Tangent
Galvanometer, Calibrating
Galvanometer by, 58
Reading Galvanometers, 76
Reading, Shielded, Dead-Beat
Galvanometers, Advant-
ages of, 78
Direction of Current, Definition of,
14
of Current in Acid, Copper,
and Zinc Voltameters, 15
of Current in Magnifying
Spring Ammeters and Volt-
meters, Indication of, 389
of Current round Magnet,
Connection between, and
Poles produced, 17
of Flow of Electric Current,
What is Meant by, 2
of Magnetic Force produced
by Current in Flat Coil,
43
Disadvantage of Magnifying Spring
Ammeter and Voltmeter,
391
Disadvantages of Cardew's Volt-
meter, 385
of Cunynghame's Ammeter and
Voltmeter, 427
of E 1 ectro - Magnetic Control
Meters, 385
of Gravity Control Meters,
392
of Permanent Magnet Meters,
376
of Siemens* Electro-dynamome-
ter, 381
of Thomson's Large Current
Galvanometer, 54
Discharge, Brush, 369
• Glow, note, 369
Multiplying Power of Shunt
used in Measuring, 349
Dispersion Photometer, 454
Distance Spark can be sent between
Balls of Influence Machine,
371
Distinction between Conduction
and Induction, 97
between Galvanometer and
Galvanoscope, note, 21
Distribution of Magnetism in Per-
manent Magnet, Measur-
ing, 24
of Power in a Circuit, 445
Disturbance, Magnetic, Shielding
Galvanometers from Ex-
traneous, 73
Drawing Cui'ves on Squared Paper,
31
Curves to Correct Results of
Experiments, 34
Dry Pile, 372
Duplex Telegraphy, Resistance
Boxes used in, 186
Dynamometer, Measuring Currents
with Siemens' Electro-, 379
Siemens' Electro-, 377, (See also
Siemens' Electro-Dynamo-
meter.)
E^
E
'ARTH, Potential of. Arbitrarily
taken as Nouorht, 84
Earth's Magnetic Force, Definition
of the Horizontal Compo-
nent of, note, 55
Ebonite Electrophorus for giving
Negative Charges, 359
Electrophorus for giving Posi-
tive Charges, 357
PUlars, Corrugating Sides of,
272
Pillars, Common Fault in Con-
structing, 272
Resistance of, 271
Specific Inductive Capacity of,
310
Edelmann's Electrometer, Sug-
gested Improvements in,
134 "
Modification of Thomson's
Quadrant Electrometer, 130
Effect of Electrolysis of Dilute Sul-
phuric Acid, 15
Eificiency Increases with Power in
Electric Lamps, 458
of Arc Light, Measuring, 455
of Current Generator, Defini-
tion of, 451
of Electric Light, Measuring,
452
of Incandesceut Lamps, 458
Elastic Curve, Definition of, 34
Electric and Heat Conductivities,
Comparison of, 158
Apparatus, Static, should be En-
closed in Mctalhc Case, 108
INDEX.
497
Electric \rc, Description of, 188, 454
Arc, Measuriug Illuminating
Power of, in any Plane, 457
Arc, Potential Dilterence Re-
quired to maintain, be-
tween Two Carbons, note,
371
Charge, 109. (See Charge.)
Circuit, Work done in, 199
Conductivity Diminishes more
Kapidly thau Heat Con-
ductivity, 159
Current. (See Current.)
Density. (See Density.)
Energy. (See Energy.)
Lamps, Description of Arc and
Incandescent, 454
Lamps, Efficiency of, Increasing
with Power, 458
Light, Measuriug Efficiency of,
452
Potential. (See Potential.)
Quantity. (See Quantity.)
bparks. (See Sparks.)
Electrical Machines, Frictional. (See
Machines. )
Machines, Influence. (See Ma-
chines.)
Units, Ohm only one yet
Legalised, 140
Electricity at Rest Resides only on
Surface of Conductor, 119
Comparing Quantities of, Gal-
vanometrically, 299
Comparing Quantities of, Stati-
cally, 111
Condensers not Stores of, but
of Electric Energy, 322
Measuring Quantity of. Abso-
lutely, 289
Positive and Negative, 85
Potential of Conductor Depends
partly on Amount of, 119
Quantity of. Defined, 109
Unit of Quantity of, 289
Quantity of, produced by Rub-
bing Two Bodies together,
115
Electrification, Amount of a Body's,
109
Exterior, No Force inside
Closed Hollow Conductor
due to, 99
Object of Rubbing Two Bodies
together to produce, 115
Electro - Dynamometer, Siemens',
377. (See also Siemens'
Electro-Dynamometer. )
Electrode, Definiti<m of, note, 131
Elecb.'olysis, Effect of, of Dilute
Sulphuric Acid, 15
Electro-Magnet, Description of, 6
O G
Electro-Magnet, Strength of, wheB
Core is Slightly Mag-
netised, 382
Magnet, Saturation of, S88
Magnetic Control Meters, 392
Magnetic Control Meters, Ad-
vantages of, 394
Magnetic Control Meters,
Crompton and Kapp's, 392
Magnetic Conti'ol Meters, Dis-
advantages of, 394
Magnetic Control Meters,
Paterson and Cooper's, 393
Electrometer, Edelmann's Modifi-
cation of Thomson's, 130
Suggested Improvements in
Edelmann's, 134
Use of, for proving Ohm's Law,
134
Rough, 94
Thomson's Absolute, Portable,
and Quadrant, 93
Weight, Lecture-room. Model
of, 88
Guard Ring for Weight, 89
Weight, Increasing Sensibility
of, by using Auxiliary High
Potential, 91
Electromotive Force, Definition of,
201,
Force, Constancy of, in
Daniell's Cell, 218
Force, Measuring Resistance
Containing, 469
Force of Cell Independent of
its Size and Shape, 211, 236
Force of Bunsen's Cell, 220
Force of Daniell's Cell, 211
Force of Grove's Cell, 218
Force of Leclanch^ Cell, 222
Force of Latimer Clark's Cell,
411
Force of Latimer Clark's Cell,
Variation of, with Tempera-
ture, 411
Force of Standard DanieU's
Cell, 412
Force of Cells in Parallel, 241
Force of Cells in Series, 241
Force of Cells partly in Series
and partly in Parallel,
241
Force Used by Deprez in Trans-
mitting Power 37 Miles,
452
Forces of Batteries, Compari-
son of, by observing Resist,
ance through which they
send Equal Currents, 231
Force of Batteries, Comparison
of, by observing their Joint
and Opposed Curx-ents, 232
498
PRACTICAL ELECTRICITY.
Electromotive Force of Current
Gonerators, Condenser
Method of Comparing, 341
Force, Measuring, 224
Electrophone Action, Compound
Interest Law of, 361—372
Electrophorus, Action of, 360
Bertsch's Rotatory, 361
Description of, 366
Ebonite, giving Negative
Charges, 359
Ebonite, giving Positive
Charges, 357
Electroscope, Calibrating Gold-Leaf,
354
Condensing, 352
Gold-Leaf, Improved Form of,
94
Indicates Potential Difference,
95
Varnishing Shade of Ordinary
Gold Leaf, 97
Electroscopes, Objections to Ordi-
nary Gold-Leaf, 96
Element, Simple Voltaic, 209
E. M, F., Meaning of, 204. (See also
Electromotive Force. )
Enclosure of Static Electric Appa-
ratus in Metallic Case
Necessary, 108
Energy, Condensers Stores of Elec-
tric, 322
Produced by Frictional Elec-
trical Machine, 352
Waste of, in Voltmeters with
High External Resistance,
422
Equivalent of Heat, Mechanical, 201
Error in Ammeters on Reversing
the Current, Testing for, 402
in Ammeters Produced by Ex-
ternal Magnetic Disturb-
ance, Testing for, 403
in Ammeters Produced by Re-
sidual Magnetism, Testing
for, 400
in Ammeters Produced by Time,
Testing for, 407
Testing Voltmeters for Heat-
ing, 415
Errors in Voltmeters, Different
Kinds of, 407
in Wattmeters, 445
Examples : 1., 12; ii. — vii., 13 ; viii.,
14 ; ix., X., 52 ; xi., 53 ; xii.
xiii.,.55; xiv.,56j xv., xvL,
67 ; xvii., 89 ; xviii., xix.,
90; XX., 91; xxi.— xxiv.,
I4.y ; XXV., 143 ; xxvi. —
xxviii., 155; xxix., 156;
XXX. — xxxiii., 158; xxxiv.,
162; XXXV.— xxxvii., 163;
xxxviii.— -xl., 180; xli. —
xliii., 201 ; xliv., 202 ; xlv.,
206; xlvi.— xlix., 207; 1.,
li., 227; Mi., liii.. 228; liv.,
232; Iv.— Ivii., 233; Iviii.—
Ix., 242; Ixi., 243; Ixii.,
247; Ixiii., Ixiv., 248; Lxv.,
249; Ixvi., 250; Ixvii.—
Ixix., 252; Ixx., Ixxi., 255;
Ixxii., Ixxiii., 256; Lxxiv.,
259; Ixxv., 260; Ixxvi.,
262; Ixxvii., 263; Ixxviii.,
264; Ixxix., Ixxx., 265;
Ixxxi., 280 ; Ixxxii.— Ixxxiv.,
281; Ixxxv., 294; Ixxxvi.,
Ixxxvii., 295 ; Ixxxviii., 297 ;
Ixxxix. — xci., 298; xcii.,
311 ; xciii. — xcv., 312 ; xcvi.,
xcvii., 313 ; xcviii., xcix.,
323; c, 325; ci., 326; cii.,
341; ciii., 350; civ., 437;
cv., cvi., 438; cvii., 439;
cviii., cix., 440 ; ex., cxi.,
443 ; cxii., cxiii., 44t; cxiv.,
446 ; cxv., cxvi., 447 ; cxvii.,
cxviii., 459; cxix,, 460;
cxx., 471 ; cxxi., 473; cxxii.,
474 ; cxxiii., 475
Examples showing Difference be-
tween Electric Potential,
Density, and Quantity, 121
Explanation of Electric Sparking,
note, 358
External Resistance, Variation of,
with Current and Poten-
tial Difference at Battery
Terminals, 204
Equality of Charges on Two Bodies
obtained by Rubbing them
together, 115
Tj^ARADAY'S Experiment on Force
in Closed Conductor due to
Exterior Electrification, 99
Farad, Definition of the, 307
Fault, Common, in Constructing
Ebonite Pillars, 272
Fibre and Pivot Suspensions, 60
Suspension used in Thomson's
Marine Galvanometer, 60
Field, Uniform Magnetic, 36
Finding Angles from their Tangents
by means of Squared Paper,
56
Tangents from their Angles
with Squared Paper, 57
the Maximum for an Expres-
sion by means of Curve, 244
Fixed E, M. F. and Resistance, Cur-
rent Developing Maximum
INDEX.
499
Useful Power with Gene-
rator with, 448
Fixed Eesistauce, Arrangement of
Cells giving Maximum
Useful Power to Conduc-
tor with, 450
Flat Coil, Direction of Magnetic
Force produced by Cur-
rent flowing in, 43
Fleming's Standai'd Daniell's Cell,
412
Flint Glass, Resistance of, 271
Specific Inductive Capacity of,
310
Flow, Wbat is meant by Direction
of, of Electric Current, 2
of Electric Current compared
with that of Water, 3, 80
Focal Length of Lens, Definition of,
456
Force, Attractive, between Two
Plane Conductors, For-
mula Connecting, with
Potential Difference and
Distance between them, 87
Definition of Lines of, 43
Definition of Horizontal Com-
ponent of Earth's Mag-
netic, note, 55
Direction of Magnetic, pro-
duced by Current flowing
in Flat Coil, 43
Electromotive. (See Electro-
motive Force. )
None Inside Closed Hollowr
Conductor due to Exterior
Electrification, 99
Foster's, Prof. G. C, Simplification
of Sine Galvanometer, 61
Frictional Electrical Machines, 352
Electrical Machines, Con-
densers for use with, 313
Fulfilment of Conditions for Tan-
gent Law in Tangent Gal-
vanometer, 43
/T-ALVANIC Cells, 209. (See also
^ Cells.)
>alvanometer, Definition of, 21
Compared with Galvanoscope,
note, 21
Constant of, 278
Absolute, 57
Astatic, Advantage of Putting
Mirror Outside Coils, 284
- — Astatic, Definition of, 282
Astatic, Thomson's, 283
— Astatic, Modified Thomson's,
284
•— Astatic, Mather's, 299
Galvanometer, Astatic, Mudford's,
105
Astatic, Damping of Vibra-
tions of Needle of, 284, 300
Ballistic, 292
Ballistic, Siemens' and Halske'a
Galvanometer Used as, 292
Dead-Beat, 78
DeHcate, 281
Delicate, Importance of being
Well Insulated, 286
Delicate, Necessity for Many
Convolutions of Wire, 281
Differential, Principle of, 148
Differential Construction of, 149
Differential, LatimerClark's,150
Differential, Best Resistance
for, 436
Differential, Inferiority of, to
Wheatstone's Bridge, 171
Differential, Mode of Adjust-
ing, 150
Differential, Use of Shunts
with, 183
Direct-Reading, 76
Direct-Reading, Adjustment to
make, 75, 78, 385, 389
Large Current, Advantage of
Low Resistance for, 136
Large Current, Deprez's, 69
Large Current, Electro-Mag-
netic Control, 392
Large Current.Gravity Control,
391
Large Current, Magnifying
Spring, 386
Large Current.Permanent Mag-
net Proportional, 75
Large Current, Thomson's Per-
manent Magnet, 53
Large Current, Spring Con-
trol, 377
Marine, 103
Marine, Fibre Suspension for,
103
Marine, Shielding, from Mag-
netic Disturbance, 103
Portable, with Approximate
Absolute Calibration, 69, 71
Potential Difference, 126
Potential Difference, Electro-
Magnetic Control, 392
Potential Difference, Gravity
Control, 391
Potential Difference, Magnify-
ing Spring, 386
Potential Difference,Permanent
Magnet Proportional, 75
Potential Difference, Spring
Control, 382
Potential Difference, Long Fine
Wire used in, 127
500
PRACTICAL ELECTRICITY.
Ralvanoraeter, Potential Difference,
when it may be Emploj'ed,
127
Potential Difference, Testing,
407
Propoi-tional, 71
Proportional, witli Permanent
Magnet Control, 73
Proportional, with Uniform
Controlling Field, 72
Quantity, Mather's Simple
Form of, 299
Reflecting, 103, 281, 293, 299
Reflecting, Deflection Propor-
tional to Current with, 108
Eeflecting, Mode of Using Lens
with, 105
Reflecting, Lamps for, 106
Reflectiiig, Mirror for, 105
Reflecting, Mather's Form of,
299
Reflecting, Mudford's Form of,
284
Reflecting, Spirit Level for, 285
Sine, 62
Sine, Foster's Simplification
of, 61
Shielded, 57, 73, 103, 390
Tangent, 36
Tangent, Simple Form of, 27
Tangent,Adjustmentof Coil of,
46
Tangent, Best Deflection to
Use with, 41
Tangent, Conditions that a
Galvanometer may he, 36
Tangent. Conditions of Tan-
gent Law Fulfilled in, 43
Tangent, Controlled Only hy
Earth'sMagnetism, Values
iu Amperes of Deflections
of, 55
Tangent, Proportions of Chan-
nel in Bobbin of, when
Tangent Law is Most Ac-
curately Fulfilled, 51
Tangent, Scale for, 38
Tangent, Sensibility of. Alter-
ing, by Removing Needle
from Plane of Coil, 62
Tangent, Sensibility of, Al-
tered by Varying Number
of Windings or Diameter
of Bobbin, 48
Calibrating, Relatively or Abso-
lutely, 22, 27, 395—400
-^ Calibi-ating, by Comparison
with Tangent Galvano-
meter, 68
Calibrating, by Sine Method, 64
-^ Calibrating, by Sine Method in
Higher Parts of Scale, 65
Galvanometer, Calibrating, by Sine
Method with Constant
Current, 67
Calibrating, by using Known
Resistances and Cell of
Constant E. M. P., 238
Calibrating, by using Known
Resistances and Constant
Potential Difference, 164
Calibration of. Unaffected by
Change in Strength of
Poles of Single Needle, 23
Sensibility of. Increasing, by
Diminishing Diameter of
Wire used in Winding, 22
Sensibility of, Modes of Vary-
ing, 229
Sensibility of, Variation of, with
Length of Wire Used in
Winding, 418
Sensibility of , Variation of, with
Resistance, 416
Sensibility of, Shunting to
Diminish, 229
Sensibility of Tangent, Varia-
tion of, 48
for Wheatstone's Bridge, Best
Arrangement of, and Bat-
tery, 171, 467
for Wheatstone's Bridge, Best
Gauge of Wire for, 172, 466
for Wheatstone's Bridge, Cur-
rent through, 465
for Wheatstone's Bridge, Mean-
ing of Deflection of, 176
Apparent Increase of Resist-
ance of, Due to Damping,
349
Best Resistance to give to, 435
Coils, Rate of Production of
Heat in, 419
Method of Measuring Resist-
ance by Loss of Charge, 348
Shielding, from Extraneous
Magnetic Disturbance, 67,
73, 103, 390
in Simple Circuit, Best Resist-
ance for, 435
and Shunt, Combined Resist-
ance of, 178
Soft Iron Core Used ip, 73
Use of Mirror with, to Avoid
Parallax, 28
and Voltameter, Relative Ad-
vantages of, 20
Galvanometer. ( See also Ammeter
Electro - Dynamometer
Voltmeter.)
Galvanoscope, Definition of, note, 21
Description of, 6
Gas-Burner, Albo-Carbon, for Gal
vanometers, note, 106
INDEX.
601
Gkis-Bumer, Eegenerative, for Gal-
vanometers, 106
Generated in Voltameter Inde-
pendent of Shape, Size, aud
Distance of Plates, 10
Eate of Production in Sul-
phuric Acid Voltameter by
One Ampere, 12
Gases, Ditference of Pressure Com-
pared with Difference of
Potential, 86, 121
Specific Inductive Capacity of,
310
Gearing, Ammeters and Voltmeters
with Magnifying, 386
Generation of Heat by Electric Cur-
rent, 192
Generator, Current, Definition of
Efficiency of, 451
Current, Measurement of
E. M. F. of, 224, 231, 234, 341
Current, Measurement of Re-
sistance of, 205, 225. 342
Current, Power Wasted in
Heating, 445
Current, Work done by, 202
Current, with Fixed E. M. F.
and Resistance, Current
Developing Maximum Use-
ful Power with, 448
Generators, Current, Forms of, 208.
{See also Cell, Batteries.)
German Silver, Change ot Resist-
ance of, with Temperature,
160
Silver, Resistance of, for Given
Length and Diameter, and
for Given Length and
Weight, 157
Silver, Resistance of, per Cubic
Centimetre and per Cubic
Inch, 154
Silver, Why Res- stance Coils
are made of, 160
Glass, Flint, Resistance of, 271
Glow Discharge, note, 369
Gold, Change of Resistance of, with
Temperature, 160
Electric and Heat Conductivi-
ties of, Compared, 159
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre and per Cubic Inch,
154
Leaf Electroscope, 94
Leaf Electroscope, Calibrating,
354
Leaf Electroscope, Objections
to Ordinary, 96
Gold-Leaf Electroscope, Varnishing
Shade of Ordinary, 97
Graduation of Ammeters, Test for
Accuracy of, 395
of Cunynghame's Ammeter and
Voltmeter, 385
of Voltmeters, Testing for Ac-
curacy of, 408. (See also
Calibrating.)
Graphically Recording Results of
Experiments, 30
Recording Results, Value of, 33
Gravity Control Meters, 391
Daniell's Cell, 212
Grove's Cell, 218
Cell, Chemical Action in, 219
Cell, E. M. F. of, 218
Cell, Resistance of, 218
Guard Ring, 89
Tube, 375
Guttapercha, Resistance of, 271
Specific Inductive Capacity of,
310
TXEAT, Amount of, per Minute
-^■*- Produced by Given Cur-
rent flowing through Given
Resistance, 199
Amount of, Pi'oduced per
Second in Coil by Constant
Current, Constancy of, 197
and Electric Conductivities,
Comparison of, 158
Conductivity Diminishes more
Rapidly than Electric, 159
Evolution of, in Conductor, by
Electric Current, 3
Generated by Electric Cur-
rent, Amount of, 192
Measuring Current by Rate of
Production of, 197
Mechanical Equivalent of, 201
Radiation, Conduction, and
Convection of, note, 195
Rate of Production of, in Gal-
vanometer Coils, 419
Heating EiTor in Voltmeters Di-
minished by Use of Outside
Resistance, 421
EiTor, None in Cardew's Volt-
meter, 426
Error, Testing Voltmeters for,
415-422
Current Generator, Power
Wasted in, 445
Property of Current, Practical
Uses of, 4
Hermetically Sealing, Definition of,
note, 20
High Resistances, Measuring, 277
502
PRACTICAL ELECTRICITY.
Higher Parts of Scale, Calibration
of, by Sine Method, 65
Potential, Definition of, 85
Hoffmann's Voltameter, 15
Holtz's Influence Electrical Ma-
chine, 367
Hooper's Vulcanised Indiarubber,
Resistance of, 271
Horizontal Component of Earth's
Magnetic Force, Defini-
tion of, note, 55
Horse-Power, 201, 443
Hydrogen, Specific Inductive Ca-
pacity of, 310
Hypotenuse, Definition of, note, 37
TLLUMINATING Power of Arc
-*- Lamp?, Measuring, 454
Power of Arc Lamps in any
Plaue, Measuring, 457
Power of Incandescent Lamps,
Measuring, 452
Image, Connection between Motion
of, on Plane Scale and
Angular Deflection of Mir-
ror, 107
Incandescent Lamp, Description of,
454
Lamp, Measuring Efficiency of,
452
Lamp, Measuring Illuminating
Power of, 452-
Lamp, Efficiency and Life of, 458
Indiarubber, Resistance of Hooper's
Vulcanised, 271
Specific Inductive Capacity of,
310
Indication of Direction of Current
in Magnifying Spring Am-
meters and Voltmeters, 389
Induction, Definition of, 97
and Conduction Compared, 97
Self, 174, 427
Inductive Action, 87
Action between Conductors of
Different Potentials, 87
Capacity, Specific, 309
IneflBciency of Frictional Electrical
Machines, 352
Inertia, Definition of Moment of,
note, 78
Infinity Plug, 151
Influence Machine, Adjusting Balls
of, to Produce Given Maxi-
mum Potential Difference,
372
— Machine, Attaching Leyden
Jars to Collectors of, 370
Machine, Compound Interest
Law of, 364, 366
Influence Machine, Condensers for
Use with, 313
Machine, Distance Spark can be
sent between Balls of, 370
Machine, Work done by, 371
Machine, Bertsch, 361
Machine, Accumulating, 361 ;
Holtz's, 367; Nicholson's,
366; Thomson's, 364; Var-
ley's, 367; Voss, 367;
Wimshurst, 367
In Parallel, Wires Joined, Defini-
tion of, 136
In Series, Wires Joined, Definition
of, 140
Instructions for Experiments, Spe-
cimens of, 476
Instruments, Commercial, for Mea-
suring Current, 79, 376
Insulating Stand, Construction of,
268
Stems, Coating, with Paraflln
Wax or Shell-lac Varnish,
267
Varnish, How to Make, note,
268
Insulation, Importance of Good,
and Mode of obtaining, in
Delicate Galvanometers,
286
Insulator, Definition of, 9
Insulators, Diminution of Resist-
ance of, with Increase of
Temperature, 271
Obtainable for Electricity, nut
for Heat, 159
Table of Resistances of, 271
Telegraph, 274
Testing, during Manufacture,
275
International Electrical Congress,
Unit of Resistance Adopted
by, 140, 141
Interpolation of Results by Means
of Curve, 34
Invariable Absolute Calibration,
Galvanometers with, 57
Iron Box, Partial Magnetic Screen,
101
Change of Resistance of, with
Temperature, 160
Electric and Heat Conductivi-
ties of. Compared, 159
Resistance, of for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Cent!'
metre, and per Cubic Inch,
154
Cores, Use of, in Galvauomo-
ters, 73 .
INDEX.
503
Iron Magnetised by Electric Cur-
rent, 3
Eesistance Coils, 162
TAB, Leyden, 314. (See also Ley-
" den Jar.)
Used for Daniell's Cell, 210
Joints, Lap and Butt, 79
Joule, Definition of the, 461
Joule's Mechanical Equivalent of
Heat, 201
K
TTEMPE'S Constant Total Cun-ent
■^^ Shunts, 257
Key, Bridge, 174
Charge and Discharge, 320
Charge and Discharge, Simple
Form of, 343
•^— Charge and Discharge, Various
Modes of Connecting, with
Condenser, Battery, and
Galvanometer, 320—322
Make and Break, Simple Form
of, 19
Plug, Description of. 139
Kirchhotf's First Law, 4o4
Second Law, 464
T ALANDE Chaperon Cell, 210
Lamps, Description of Arc and
Incandescent, 454. (See
also Arc, Incandescent.)
Lamps Used with Reflecting Galva-
nometer, 105
Lap Joint, 79
Large Potential Differences, Pro-
duction of, 351
Latimer Clark's Cell, 410
Clark's Cell, Constancy of
E. M. P. of, 411
Clark's Cell, E. M. F. of, 411
Clark's Cell, Temperature Va-
riation of E. M. F. of, 411
Clark's Differential Galvanome-
ter, 150
Law connecting Two Sets of Facts
Determined by means of
Curve, 35
of Differential Galvanometer,
14S. 183
— — Experimental Proof of Ohm's,
130
Kirchhoff's First, 464
Kirchhoff's Second, 464
Ohm's, 130
Tangent, Fulfilment of Condi-
tions for, in Tangent Gal-
vanometer, ^S
Law, Tangent, When True, 41
Sine, When True, 61
of Wheatstone's Bridge, 167
Laws of Surface Leakage and Leak-
age through the Mass, 270
Lead, Change of Resistance of, with
Temperature, 160
Electric and Heat Conducti-
vities of. Compared, 159
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Leakage, Dependence of Rate of
Loss of Charge from, on
Dielectric Only, 348
Surface, 266
Surface, Law of, 270
through the Mass, 266
through the Mass, Law of, 270
Leclanchd Cell, 220
Cell, Chemical Action of, 221
Cell, E. M. F. of, 222
Legal Ohms and B. A. Units, Equa-
tion Connecting, 142
Unit of Resistance, 140
Length, Variation of Resistance
with, 143
Lens, Definition of Focal Length
of, 456
Mode of Using, with Reflecting
Galvanometer, 104, 105
Levels, Spirit, for Reflecting Gal-
vanometer, 285
Leyden Jar, Attaching, to Collecting
Combs of Electrical Ma-
chines, 370
Jar, Construction of, 314
Jars, Battery of, 317
Life of Incandescent Lamps, 458
Light, Measuring Efficiency of Elec-
tric, 452
Measuring Illuminating Power
of Electric, 452
Lines of Force, Definition of, 43
Liquid and Wire Resistances, Com-
parison of Use of, IM
Decomposed by Electric Cur-
rent, 3
Saturation of, note, 411
Super-saturation of, note, 411
Liquids, Diff"erence of Level in. Com-
pared with Difference ol'
Potential, 86
Local Action in Cell, 217
Action in Daniell's Cell, How
to Prevent, 217
504
PRACTICAL ELECTRICITY
Lockwood Cell, 213
Logarithmic Decrement, 296
Decrement, Determination of,
■when Damping is Very
Slight, 297
Lord Eayleigh, Silver Voltameter
used hy, 11
M
TVTACHINES, Electrical, Adjust-
-"■'- ing Balls to Produce Given
Potential Difeerence, 372
Electrical, Attaching Leyden
Jars to Collectors of. 370
Electrical, Condensers for Use
with, 313
Electrical, Frictional, 352
Influence, Bertsch's, 361
Influence, Accumulating, 361 ;
Holtz, 367; Nicholson's,
366; Thomson's, 364; Var-
ley's, 367; Voss, 367;
"Wimshurst, 367
^— Influence, Accumulating, Con-
densers for Use with, 313
—— Influence, Accumulating, Com-
pound Interest Law of,
364, 366
Influence, Accumulating,
Work done by, 371
Magnet, Connection between Poles
of, and Di. action of Cur-
rent round, 17
Definition of North-Seeking
End of, note, 16
Deflected by Current, 3
Electro. {See Electro-Magnet. )
Motion of, Produced by Uni-
form Magnetic Field, 390
— Permanent, Measurement of
Distribution of Magnetism
in, 24
Permanent, Proportional Gal-
vanometer Controlled by,
73
Magnets, Position of Poles in, 23
Magnetic Axis of Needle, Definition
of, 37
Disturbance, Shielding Galva-
nometers from Extraneous,
57, 73, 103, 390
Effect of Bobbin, Variation of,
with Current and Resist-
ance, 418
— — Field, Motion of Magnet pro-
duced by Uniform, 390
— — Force, Definition of Horizontal
Component of Earth's,
note, 55
—— Force, Direction of, produced
by Current in Flat Coil, 43
Magnetic Meridian, Definition ol
Plane of, note, 45
Property of Current, Practical
Uses of, 4
Saturation, 388
Screen, Thick Iron Box, 101
Magnetised, Iron, by Current, 3
Magnetism, Measurement of Dis-
tribution of, in Permanent
Magnet, 24
Residual, Definition of, 385
Residual, Testing Ammeters
for, 400
Magnifying Gearing, Ammeters and
Voltmeters with, 383
Spring Ammeter and Volt-
meter, 386
Spring Ammeter and Volt-
meter, Adjustment for Sen-
sibility in, 389
Spring Ammeter and Volt-
meter, Advantages of, 390
Spring Ammeter and Volt-
meter, Disadvantage of, 391
Spring Ammeter and Volt-
meter, Indication of Di-
rection of Current in, 389
Spring Voltmeter, Best Law of
Variation for Gauge of
Wire in, 421
Making Sine Scale, Mode of, 68
Tangent Scale, Mode of, 38
Mance's Test for Resistance Con*'
taining E. M. F., 470
Marine Galvanometer, 103
Galvanometer, Fibre Suspen-
sion used in, 60
Galvanometer, Shielding, from
Magnetic Disturbance, 103
Mass, Law of Leakage through, 270
Leakage through, 266
Material for Outside Resistance for
Voltmeters, 422
for Wire for Voltmeter Coils,
420
used in Resistance Coils, 159
Variation of Resistance with,
146
Mather's Mode of Calibrating Gal-
vanometer with Constant
Current, 67
Proportional Galvanometer
with Uniform Controlling'
Field, 72
Reflecting Galvanometer, 299
Matthiessen's Equt;tiou Connecting
Resistance with Tempera-
ture, 153
Experiments, Tables deduced
from, 154, 157
Maximum, Finding, by means of
Curve, 244
INDEX.
505
Maximum Potential Difference of
Electrical Machine, Deter-
mination of, 372
Useful Power, Current that
Develops, 448
Useful Power in Generator
with Fixed E. M. F. and
Kesistauce, Current that
Develops, 448
Measuring Arc Light, Efficiency of,
455
Arc Light, Illuminating Power
of, in any Plane, 457
«^— Are Light, Illuminating Power
of. How to Overcome Dif-
ference in Colour between
it and Candle when, 457
Efficiency of Electric Light, 452
^■^ Efficiency of Incandescent
Light, 452
Current, Alternating, 198
Current, Commercial Instru-
ments for, 79, 376
Current, by Eate of Production
of Heat, 197
Current with Siemens' Dyna-
mometer, 379
Small Currents, Disadvantas-e
of using Voltameters for,20
Strength of Current, 4
Distribution of Magnetism in
Permanent Magnet, 24
Electric Density by means of
Proof Plane, 117
Electromotive Force of Cur-
rent Generators, 224, 2?1,
234, 341. (See also Electro-
motive Force.)
Potential Difference by Weigh-
ing, 88
Potential Differences, Alter-
nating, 426
Potential Differences, Static
and Current Methods of.
Compared, 125
Power, 442
Resistance of Batteries, 205, 225
Resistance of Batteries using
Known Resistances, 226
Resistance of Batteries using
Known Resistances and
Shunt, 226
Resistance of Current Gener-
ator, Condenser Method
of, 312
Resistance by Rate of Loss of
Charge, 344
Resistance by Rate of Loss of
Charge, Galvauometric
Method of, 3 18
Resistance Containing E.M.F.,
Measuring Resistance during Paa-
sage of Strong Current, 187
High Resistances, 277
Specific Inductive Capacity,
332
Quantity of Electricity, 111,
289, 299
Measureinpiit Absolute, of Capa-
city, 327
of Poieutial Compared with
Measurement of Tempera-
ture, 85
Mechanical Equivalent of Heat, 201
Meidinger Cell, 212
Mercury, Change of Resistance of,
with Temperature, 160
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Meridian, Definition of Plane of
Magnetic, note, 45
Metal having Least Change of Re-
sistance with Tempera-
ture, 160
Metals, Change of Resistance of,
with Temperature, 160
Electric and Heat Conducti-
vities of. Compared, 159
^— Resistance of, for Given Length
and Diameter, or for Given
Length and Weight, 156
Resistance of, per Cubic Centi-
metre, and per Cubic Inch^
153
Metallic Case, Necessary Enclosure
of Electric Apparatus in,
108
Meters, Electro-Magnetic Control,
392
Electro-Magnetic Control,
Crompton and Kapp's, 392
Electro-Magnetic Control, Pa-
terson and Cooper's, 393
Electro-Magnetic Control, Ad-
vantages of, 394
Electro - Magnetic Control,
Disadvantages of, 394
Gravity Control, 391
Spring Control, 377
Spring Control, Cunynghame's,
382 ; Magnifying, 386 ;
Siemens', 377
Meters. (See also Ammeter, Dyna-
mometer, Galvanometer,
Photometer, Voltmeter,
Wattmeter.)
Metre Bridge, 168
Mica, Resistance of, 271
506
PRACTICAL ELECTRICITY.
Mica, Specific Inductive Capacity
of, 310
Micrometer Screw, Description of,
note, 24
Minotto's Cell, 211
Mirror, Angular Motion of, Half
that of Reflected Eay, 106
Connection between Angular
Deflection of, and Motion
of Image on a Plane Scale,
107
in Galvanometer, Use of, to
Avoid Parallax, 28
for Reflecting Gal vanometer,105
Moment of Couple, Definition of,
note, 283
of Inertia, Definition of, note, 78
Motion, Angular, of Reflected Ray,
lOG
of Image on Plane Scale, Con-
nection between, and Angu-
lar Deflection of Mirror, 107
of Magnet produced by Uni-
form Magnetic Field, 390
Multiples of Ohm, Construction of,
145
Multiplying Power of Shunt, 178
Power of Shunt used in
Measuring a Discharge, 3 19
N
"NTAPIERIAN Logarithmic De-
crement, 296
Negative Charges, Ebonite Electro-
phorus Arranged to Give,
359
Electricity, 85
Network, Currents in, 462
Nicholson's Revolving Doubler, 366
Nickel, Resistance of, pqr Cubic
Centimetre, and per Cubic
Inch, 154
North-seeking end of Magnet, Defi-
nition of, note, 16
Nought, Potential of Earth Arbi-
trarily taken as, 84
Null Methods, Meaning of, 236
r)HM, 89, 140, 141
^^ Construction of Multiples
of, 145
Definition of Legal, 140
Only Electrical Unit yet Legal-
ised, 140
Ohmmeter, Description of, 190
Ohms, Legal, and B. A. Units, Equa-
tions connecting, 142
■ Wires having Resistance of
about Ten, 143
Ohm's Law, 130
Law, Experimental Proof of, 130
Olefiiant Gas, Specific Inductive
Capacity of, 310
DARAFFIN WAX, Coating In-
sulating Stems with, 267
Wax, How to Prevent Over-
heating when MeltLug, note,
267
Wax, Resistance of, 271
Wax, Specific Inductive Capa-
city of, 310
Parallax, Definition of, note, 28
Mirror Used in Galvanometer
to Avoid, 28
Parallel, Cells in. Figure of, 239
Cells in, Symbolical Repre-
sentation of, 240
Circuit, Wires Joined in, 136
Circuit, Independence of Cur-
rents in, 260
E. M. F. of Cells in, 241
Resistance, 179
Paterson and Cooper's Electro-Mag-
netic Control Meters, 393
P. D., Meaning of, 230
Periodic Time of Vibration, Defini-
tion of, 291
Permanent Magnet, Proportional
Galvanometers Controlled
by, 73
Magnet, Measurement of Dis-
tribution of Magnetism in,
24
Magnet Meters, 69
Magnet Meters, Advantages
of, 78'
Magnet Meters, Direct-Read-
ing, 76
Magnet Meters, Disadvantage
of, 376
Magnet Meters, Proportional,
71
Photometer, Dispersion, 454
Rumford's, 452
Pivot and Fibre Suspensions, 60
Plane of Magnetic Meridian, Defini-
tion of, note, 45
Proof, 116
Platinoid, 160
Resistance of, 161
Resistance, Coils of, 161
Platinum, Electric and Heat Con-
ductivities of, Compared,
159
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
INDEX
507
Platinum, Besistance of, per Cubic
Centimetre, and per Cubic
Inch, 154
Silver Alloy, Change of Resist-
ance of, with Temperature,
160
Silver Alloy, Resistance of, for
Given Length and Dia-
meter, and for Given
Length and "Weight, 157
Silver Alloy, Resistance of per
Cubic Centimetre, and per
Cubic Inch, 154
Plug, Infinity, 151
Key, Description of, 139
Resistance Boxes, Construction
of, 151
Poggendorffs Method of Compar-
ing E.M.Fs., 234
Method, Use of, for Calibrating
Voltmeters, 413
Polarisation of Darnell's Cell, 216
of Latimer Clark's Cell, 411
Poles of Magnet, Connection be-
tween, and Direction of
Current round Magnet,
17
of Magnets, Positions of, 23
Portable Electrometer, 93
Galvanometer with Approxi-
mate Absolute Calibration,
Positive Electricity, 85
Potential, 85
Potash Bichi-omate Cell, 222
Bichromate Cell, Chemical Ac-
tion in, 223
Bichromate Cell, Composition
of Liquid for, 222
Bichromate Cell, E. M. F. of,
223
Bichromate Cell, Form of Zinc
for, 223
Potential of Conductor Compared
with Pressure of Gas, 121
of Conductor, Ways in which
it can be Varied, 121
of Conductor Depends partly
on Amount of Electricity
on it, 119
of Conductor Depends partly
on its Position, 119
of Conductor Depends partly
on its Shape, 119
Density, and Quantity, Exam-
ples showing Difference be-
tween, 121
Diiference, 80
Difference, Adjusting Balls of
Electrical Machine to Pro-
duce Given Maximum,
S72
Potential Difference, Alternating,
Increases Practical Resist-
ance of Voltmeters, 427
Difference, Alternating,Measur-
ing, 426
Difference between Two Con-
ductors does not Measure
Difference in their Electric
Charges, 85
Difference between Two Points
in Uniform Conductor Con-
veying Current Propor-
tional to Distance between
Points, 83, 143
Diflference, Charges on Two
Conductors Vary as, for
Constant Relative Posi-
tions, 109
Difference Compared with Dif-
ference of Level in Liquids,
86
Difference Compared with Dif-
ference of Pressure in
Difference Compared with Dif-
ference of Pressure of
Water Plowing in Pipe,
80,81
Difference, Contact, 351
Difference, Distance and At-
traction between Two Par-
allel Plane Conductors, 87
Difference Galvanometer, Ab-
solutely Calibrated, 127,
408—423
Difference Galvanometers,
Long Fine Wire Used in,
127
Difference Galvanometer, when
it may be Employed, 127
Difference, Increasing a, in
known Ratio, 354
Difference, Large, Arrangement
of Cardew's Voltmeter for
Measuring, 425
Difference, Large, Production
of; 351
Difference,Measuring by Weigh-
ing, 88
Difference Method of Com-
paring Resistances, 140
Difference, Ratio of, to Current
Constant for Given Con-
ductor, 130
Difference, Ratio of, to Current
is Resistance, 130
Difference Required to Main-
tain Electric Arc between
Two Carbons, note, 371
Difference Required to Pro-
duce Spark between Point
and Plate, 371
508
PKACTICAL ELECTRICITY.
Potential Difference Eeqnired to
Produce Spark between
Two Metallic Balls, 370
Difference, Static and Current
Method of Measuring,
Compared, 125
Difference, Sub-dividing into
Known Fractions, 278
Difference, Variation of, at Bat-
tery Terminals, with Varia-
tion of Current, 204
Difference, Variation of, with
Resistance of Given Volt-
meter to Produce Given
Deflection, 419
Higher, and Lower, Positive,
and Negative, Definition
of, 85
— — Increasing Sensibility of
Weight Electrometer by
Using Auxiliary High, 91
Inside Closed Conductor, 98
1 Measurement of. Compared
with Measurement of Tern-
perature, 85
of Earth Arbitrarily taken as
Nought, 84
Uniform on Conductor, 86
Uniform in Conductor, 98
Power, Arrangement of Cells Giv-
ing Maximum Useful, to
Conductor of Fixed Resist-
ance, 450
Current Developing Maximum
Useful, with Generator of
Fixed E. M. F. aud Resist-
ance, 418
Definiti. n of, 441
Distribution of, in Circuit, 445
E. M. F. used by Deprez in
Transmitting, 37 Miles,
452
Horse, 201, 443
Measurement of, 442
Unit of, 442
Utilised in Circuit Outside Ge-
nerator, 445
Wasted in Heating Generator,
446
Pieparation of Varley's Carbonised
Cloth, 397
Pressure, Difference of, in Gases,
Compared with Difference
of Potential, 86
—^ of Gas Compared with Poten-
tial of Conductor, 121
— of Water, Difference of, in Pipe
Compared with Difference
of Potentials, 81
Proof of Ohm's Law, Experimental,
130
Proof-plane, 116
Proof-pMhe, Measuring Electric
Density by means of, 117
Properties of Electric Current, 3
of Electric Current, Practical
Uses of, 4
Proportional Coils of Wheatstone's
Bridge, 172
Galvanometer, 71, 75, 108, 389
Proportions of Channel in Bobbin
of Tangent Galvanometer,
when Tangent Law is Most
Accurately Fulfilled, 61
Q
QUADRANT Electrometer, Thom-
son's, 93
Electrometer, Edelmann's Mo-
dification of Thomson's,
130
Electrometer, Edelmann's Mo-
dification of Tnomson's,
Defects in, 134
Electrometer, Edelmann's Mo-
dification of, Dry Pile for,
133, 372
Electrometer, Edelmann's Mo-
dification of. Needle for,
132
Electrometer, Formula for, 134
Quantities of Electricity, Compari-
son of. 111, 299
Quantity of Electricity, Definition
of, 109. {See also Charge.)
of Electricity, Unit of, 289
of Electricity Produced by
Rubbing Two Bodies To-
gether, 113
Potential, Density, Examples
showing Difference be-
tween, 121
Unit of, 289
RADIATION of Heat, Explanation
-*-^ of, note, 195
Rate of Loss of Charge, Measuring
Resistance by, 344
of Production of Heat in Gal-
vanometer Coils, 419
of Production of Heat, Mea-
suring Current by, 197
Ratio of Potential Difference to
Current Constant with
Given Conductor, 130
of Potential Difference to Cur-
rent is the Resistance, 130
of Sensibilities of Commuta-
tor Ammeter in Parallel
and in Series, 431
INDEX.
509
Ratio ot Sensibilities of Voltmeter in
Parallel and in Series, 433
Rayleigli, Lord, Silver Voltameter
Used by, 11, 395
Lord, Temperature Variation
of E. M. P. of Clark's Cell
Determined by, 411
Eecordinp Results of Experiments
Graphically, 30
Results of Experiments Gra-
phically, Value of Curves
for, 33
Reflected Ray, Angular Motion of ,106
Reflecting Galvanometer, 103, 281,
293, 299. {See also Galva-
nometer, Reflecting.)
' Galvanometer, Diff"erent Ways
of Forming Ima^e with, 105
Galvanometer, Lamp Used
with, 106
Galvanometer, Modes of Using
Lens with, 105
Galvanometer, Spirit Level
for, 285
Relative Cahbration of Galvano-
meter, Meaning of, 22
Relatively Calibrating Galvanome-
ters, 27
Replenisher, Thomson's, 364
Representation of Batteries, Sym-
bolical, 173, 240
Residual Magnetism, Definition of
note, 388
Magnetism, Testing Ammeters
for, 400
Resin, Specific Inductive Capacity
of, 310
Resistance, 9, 129
Amount of Heat produced per
Minute by Given Current
flowing through Given, 199
and Current, Variation of Mag-
netic Effect of Bobbin
with, 418
Apparent I^fPtease of, in Gal-
vanometer, Due to Damp-
ing, 349
of Battery, Measuring, 205, 225,
342
Best, for Differential Galvano-
meter, 436
Best, for Galvanometer in Sim-
ple Circuit, 435
Best, for Galvanometer of
Wheatstone's Bridge, 172,
466
Best, for Coils of "Wheatstone's
Bridge, 171
^— Best, to Give to Galvanometer,
435
Box, Description of, 28
— Bo.x, Construction of Plug, 151
Resistance Box, Construction of
Sliding, 186
Box used in Duplex Telegraphy,
187
Resistances, Calibrating Galvano-
meter by Using Kno wn , a nd
Constant Potential Differ-
ence, 164
Calibrating Galvanometer by
Using Known, and Cell of
Constant E. M. F., 238
Change of, with Temperature,
Results of Matthiessen's
Experiments on, 160
Comparing, 136
Comparing, Differential Galva-
nometer Method of, 148
Comparing, Potential Differ-
ence Method of, 140
Comparing, Simple Substitu-
tion Method of, 138
Comparing, Wheatstone's
Bridge Method of, 166
Comparing Use of Liquid and
Wire, 194
Resistance Containing E. M. F,,
Measuring, 469
Coils, 28, 145, 151, 153, 159, 163
Coils, Accurate Standard, 162
Coils, Construction of, 145
Coils Heating with Strong Cur-
rent, 192
Coils, German Silver, 160
— Coils, Iron, 162
Coils, Platinoid, 161
Coils, Platinum- Silver Alloy,160
Coils, Materials used in, 169
Coils, Modes of Winding, 163
Coils, Temperature Variation
of, 153
Increase of, by Self-induction,
427
of Current Generator, Conden-
ser Method of Measuring,
342
of Darnell's Cell, 211
of Grove's Cell, 218
of Insulators, Diminution of,
with Increase of Tempera-
ture, 271
of Insulators, Measuring, 275
of Insulators, Table of, 271
of Insulator to Sparking, 311,
370, note, 358
Law of Variation of, with Tem-
perature, 152
Measuring, by Rate of Loss of
Charge, 314, 348
Measuring, Containing E.M.F.,
469
Measuring, - during Passage of
Strong Current, 187
510
PRACTICAL ELECTRICITY.
Resistance, Measuring High, 277
Metal having Least Change of,
with Temperature, 160
ParaUel, 179
of Galvanometer and Shunt
Combined, 178
of Metals for Given Length and
Diameter, or for Given
Length and Weight, 156
— of Metals per Cuhic Centimetre,
and per Cubic Inch, 153
of Platinoid, 161
per Cubic Centimetre, and per
Cubic Inch Compared, 348
Proportional to Ratio of Poten-
tial Difference to Current,
130
should be High in Potential
Difference Galvanometers,
137
should be Low in Current Gal-
vanometers, 136
Unit of, British Association, 141
Unit of, Legal, 140
Unit of, Siemens', 142
— Variation of, with Length, 143
Variation of, with Material, 146
— Variation of, with Sectional
Area, 146
— Variation of, with Temperature,
147, 152
Variation of Sensibility of Gal-
vanometer with, 416
Variation of Sensibility of
Voltmeter with, 407, 418
Voltmeters with Outside, 421
Results of Experiments Corrected
by Drawing Curves, 34
of Experiments, Graphically
Recording, 30
of Experiments, Value of
Curves in Graphically Re-
cording, 33
Interpolation of, from Curve, 34
Retardation, Definition of, 331
Reversing Current without Alter-
ing its Value, 47
Revolving Doubler, Nicholson's, 366
Ring, Guard, 89
Ross Cell, 210
Rotatory Electrophorus, 361
Rough Experiments, Candles to use
in the place of Standard
Candles for, 452
Rubbing Two Bodies together,
Quantity of Electricity
Produced by, 113
Two Bodies together to Pro-
duce Electrification, Ob-
ject of, 115
Two Bodies together. Equality
of Charges Obtained by, 115
Rumford's Photometer, 452
Rymer Jones' Constant Total Cur-
rent Shunts, 259
S
SATURATION, Magnetic, 388
^ of Liquid, Definition of, 411
Safety Arrangement with Com-
mutator Ammeter, 432
Scale, Connection between Motion
of Image on Plane, and
Angular Deflection of Mir-
ror, 107
for Tangent Galvanometer, 39
Mode of Mating Tangent, 39
Scales, Accuracy of Readings with
Degree and Tangent Com-
pared, 40
Screen, Magnetic, Thick Iron Box,
101
Screw, Micrometer, Description of,
note, 24
Sealing Hermetically, Definition of,
note, 20
up One End of Cable when
under Test, 268
Secondary Batteries, Small Internal
Resistance of, 206, 261
Batteries, Use of, in Electric
Lighting, 261
Sectional Area, Variation of Resist-
ance with, 146
Self-induction, 174, 427
Induction, Small, in Cardew's
Voltmeter, 427
Sensibilities of Commutator Am-
meter, Ratio of, in Parallel
and in Series, 431
of Commutator Voltmeter,
Ratio of, in Parallel and
in Series, 433
Sensibility, Adjustment for, in
Magnifying Spring Am-
meters and Voltmeters, 389
of Galvanometer, Variation of,
21, 48, 229
of Galvanometer, Variation of,
with Length of Wire used
in Winding, 418
of Galvanometer, Variation of,
with Resistance, 416
of Tangent Galvanometer Al-
tered by Removing Needle
from Plane of Coil, 52
of Tangent Galvanometer Al-
tered by Varying Number
of Windings or Diameter
of Bobbin, 48
of Voltmeters, Variation of,
with Change of Resistance,
407.418
INDEX.
511
Sensibility of Wheatstone's Bridge,
Conditions affecting,171,466
of Wheatstone's Bridge, Mode
of Increasing, 168
of Weight Electrometer, In-
creasing, by Using Auxili-
ary High Potential, 91
Shunting Galvanometer to
Diminish, 229
Testing Ammeters for Perma-
nent Alteration of, 407
Two Degrees of, in Commutator
Ammeter and Voltmeter,
427
Series, E. M. P. of Cells in, 241
Cells in. Figure of, 239
Cells in. Symbolical Repre-
sentation of, 240
Wires Joined in, 140
Several Currents Meeting at a
Point, Law Connecting, 464
Shell-lac, Resistance of, 271
lac Specific Inductive Capa-
city of, 310
lac Varnish, Coating Insu-
lating Stems with, 267
lac Varnish, Preparation of,
note, 268
Shielded, Dead-Beat, Direct-Read-
ing Galvanometers, Advan-
tages of, 78
Shielding Galvanometers from Ex-
traneous Magnetic Disturb-
ance, 57, 73, 103, 390
Short-Circuited, Definition of, 217
Shunts, 59, 177, 183, 253
Shunt Box, Construction of, 181
Shunts, Constant Total Current, 257
Shuntand Galvanometer, Combined
Resistance of, 178
Increase of Total Current pro-
duced by Use of, 183, 253
Measuring Resistances of Bat-
teries by means of, 226
Multiplying Power of, 178
Multiplying Power of, when
Used in Measuring Dis-
charge, 349
Shunts, Use of, with Differential
Galvanometer, 183
Shunt, Use of, with Wheatstone's
Bridge, 176
Shunting Battery only while Charg-
ing Condenser, Arrange-
ment for, 343
Galvanometer to make it Less
Sensitive, 229
Siemens' Electro-Dynamometer, 377
Electro-Dynamometer, Advan-
tages of, 380
' — Electro-Dynamometer, Disad-
vantages of, 381
Siemens* Electro - Dynamometer,
Measuring Current with,
379
Electro-Dynamometer as Stan-
dard Instrument, 382
Siemens' Unit of Resistance, 142
Silver, Change of Resistance of,
with Temperature, 160
Electric and Heat Conductivi
ties of. Compared, 159
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Chloride Battery of De la Rue
and Hugo MttUer, 314
Voltameter, Description of,
note, 11, 395
Voltameter, Precautions in
Using, note, 11
Voltameter, Use in Calibrating
Ammeters, 395—400
Voltameter Used by Lord
Rayleigh, 11, 395
Voltameter, Weight of Silver
Deposited on Plate of, per
Second, by One Ampere, 11
Similarly Charged Bodies ; Reason
they Fly from One An-
other, 340
Simple Substitution Method of
ComparingResistances, 138
Voltaic Element, 209
Sine, Definition of, note, 38
Galvanometer, 62
Galvanometer, Foster's Simpli-
fication of, 61
Law, Conditions under which it
is True, 61
Law, How Conditions of, are
Fulfilled in Sine Galvano-
meter, 62
Method, Calibrating Galvano-
meter by, 64
Method of Calibrating Galvano-
meter with Constant Cur-
rent, 67
Method of Calibrating Higher
Parts of Scale, 65
Scale, Method of Making, 68
Sliding Resistance Boxes, 186
Small Current, Disadvantage of
using Voltameter to Mea-
sure, 20
Soft Iron Cores used in Galvano-
met(!rs, 73
Solenoid, Definition of, note, 387
Sparking, Resistance to, of Insu>
lators, 311, note, 358
512
PRACTICAL ELECTRICITY.
Spares be b ween Balls of Electrical
Machines, Length of, 370
Electric, 358
Potential Difference Eequired
to Produce, between Point
and Plate, 371
Potential Ditterence Eequired
to Produce, between Two
MetalUc Balls, 370
Sphere, Capacity of, in Space, 339
Spherical Condenser, Capacity of,
338
Spirit Levels forEeflecting Galvano-
meters, 285
Specific Inductive Capacity, Defini-
tion of, 309
Inductive Capacity of Solids
and Liquids, 310
Inductive Capacity, Measuring,
33 i
Specimens of Instructions for Ex-
periments, 476
Sprin? Control Meters, 377
Control Meters, Cunyng-
hame's, 382
Control Meters, Magnifying,
386. (See also Magnifying
Spring Ammeter and Volt-
meter.)
Control Meters, Siemens', 377
Squared Paper, Drawing Curves on,
31
^— Paper, Meaning of Inaccura-
cies in Ciu-ves Drawn on,
33
Paper, Selection of Suitable
Units on, 31
Paper, Use of, 30
Paper, Using, to Find Angles
from their Tangents, 56
Paper, Using, to Find Tangents
from their Angles, 67
Standard Air Condenser, 334
Candle, Description of, 452
Cells, 410
Daniell's Cell, 411
Daniell's Cell, E. M. F. of, 412
DanieU's Cell, Fleming's, 412
Voltmeter, 422
Static and Current Methods of
Measuring Potential Dif-
ferences Compared, 125
— Electric Apparatus, Necessary
Enclosure of, in Metallic
Case, 108
Statical Method of Comparing
Capacities, 330
Stems, Coating Insulating, \?ith.
Paraffin Wax or Shell-lac
Varnish, 267
Storage Cells, Small Internal Re-
sistance of. "261
Storage Cells, Measuring Resistance
of, 206
Strength of Current, Measurement
of, 4
of Current, Why Measured by
Chemical Property, 10
of Electro - Magnet, Law of,
when Core is Slightly Mag-
netised, 382
of Poles of Single Needle of
Galvanometer, Calibration
Unaffected by, 23
Striking Distance, Definition of,
note, 371
Strong Current, Measuring Eesist-
ance during Passage of, 187
Subdividing Potential Difference
into Known Fractions, 278
Submarine Cable, Capacity of, 309
Substitution, Simple, Method of
Comparing Eesistances, 138
Sulphur Dioxide, Specific Inductive
Capacity of, 310
SpecificInductiveCa.pacityof,310
Sulphuric Acid, Dilute, Effect of
Electrolysis of, 15
Acid Voltameter, Construction
of, 18
Acid Voltameter, Description
of, 6
Acid Voltameter, Objection to
Ordinary Form of, 18
AcidVoltameter, Volume of Gas
produced in, per Second,
by one Ampere, 12
Acid Voltameter,Weight of Gas
produced in, per Second,
by one Ampere, 22
Super-saturation of Liquid, Defini-
tion of, note, 411
Surface Leakage, 266
Leakage, Law of, 270
of Conductor, Electricity at
Rest Eesides Only on, 119
Suspension, Fibre, used in Thom-
son's Marine Galvanome-
ter, 60
Suspensions, Pivot and Fibre, Com-
pared, 60
Symbolical Representation of Bat-
teries, 173, 240
^ABLE of Electric and Heat
Conductivities, 159
— of Eesistances of Insulators,
271
— of Eesistances for a Given
Length and Diameter, or
for a Given Length and
Weight, 157
INDEX.
613
Table of Resistances of Metals per
Cubic Centimetre, and per
Cubic Inch, 154
~— of Specific Inductive Capaci-
ties, 310
of Temperature Variation of
Resistance, 160
showing Potential, Density,
and Quantity of Electricity
on Conductor in Different
Conditions, 123
showing Variation of External
Resistance, Current, and
Potential Difference at
Battery Terminals, 205
Tangent of Angle of Deflection
Proportional to Current in
Tangent Galvanometer, 43
• Definition of, note, 37
and Degree Scales, Accuracy of
Readings Compared, 40
Galvanometer, 36
— Gralvanometer, Alteration of
Sensibility of, by Altering
Position of Needle, 51
Galvanometer, Adjustment of
Coil of, 46
Galvanometer, Best Deflection
to Use with, 41
Galvanometer, Calibration of
Galvanometer by Direct
Comparison with, 58
Galvanometer, Conditions to
be Fulfilled in, 36
Galvanometer, Controlled Only
by the Earth's Magnetism,
Values in Amperes of De-
flections of, 55
Galvanometer, Fulfilment of
Conditions for Tangent
Law in, 43
Galvanometer, Proportions of
Channel in Bobbin of,when
Tangent Law is Most Ac-
curately Fulfilled, 51
Galvanometer, Scale for, 39
Galvanometer, Simple Form
of, 27
Law, How Conditions of, are
Fulfilled in Tangent Gal-
vanometers, 43
Law, When True, 41
Scale, Mode of Making^ 38
Tangents, Finding Angles from, by
means of Squared Paper, 56
Telegraph Insulators, 274
Insulators, Testing during
Manufacture, 275
Telegraphy, Resistance Boxes used
in Duplex, 187
Telephone, Description of the Bell,
336
H H
Temperature, Change of Resistance
with. Results of Matthies-
sen's Experiments on, 160
Curve, Cooling Correction of
Observed Rise of, 196
Diminution of Resistance of
Insulators with Increase
of, 271
Equation connecting Variation
of Resistance of Metals
with, 153
■ Law of Variation of Resistance
with, 152
• Measurement of, Compared
with Measujement of Po-
tential, 85
Variation of E. M. F. of Lati-
mer Clark's Cell, 411
Variation of Resistance with,
147
Testing Ammeters, 394
Ammeters for Accuracy of
Graduation, 395
Ammeters for Error on Re-
versing the Current, 402
Ammeters for Error Produced
by External Magnetic Dis-
turbance, 403
Ammeters for the Permanent
Alteration of Sensibihty,
407
Ammeters for Residual Mag-
netism, 400
Cables, Sealing up One End
while, 268
Insulators during Manufao-
ture, 275
Voltmeters, 407
Voltmeters for Accuracy of
Graduation, 408
Voltmeters for Healing Error,
415
Testing. ( See also Comparing, Mea-
suring. )
Thompson's, Prof. Silvanus P., Rule
for Best Dimensioas of
Channel of Bobbin of Tan-
gent Galvanometer, 61
Thomson's, Sir William, Arrange-
ment for Increasing a
Potential Difference in
Known Ratio, 354
Astatic Gralvanometer, 283
Astatic Galvanometer, Modi-
fied Form of, 284
Electrometers, 93
Electrometer, Edelmann's
Form of, 130
Large Current Galvanometer,
53
Leyden Jar, 315
Marine Ghilvanometer, 103
5U
PRACTICAL ELECTRICITY.
Thomson's, Sir "William, Marine
Galvanometer, Fibre Sus-
pension used in, 60
Marine Galvanometer, Sliield-
ing, from Magnetic Dis-
turbance, 103
Reflecting Galvanometer, 283
Replenisher, 364
Time Rise of Temperature due to
Passage of Current, 195
Tin, Change of Resistance of, with
Temperature, 160
Electric and Heat Conductivi-
ties of, Compared, 169
Resistance of , for Given Length
and Diameter, and for
Given Length andWeight,
157
Resistance of, per Cubic Cen-
timetre, and per Cubic
Inch, 154
TTNIFORM ControlUng Field,
^ Proportional'Galvanometer
with, 72
Magnetic Field.Definition of, 36
Magnetic Field, Motion of
Magnet Produced in, 390
Potential on Conductor, 86
Unit of Capacity, 307,
of Current, 11
of Density, 117
of Potential D.fFerence, 89, 141
of Power, 442
of Quantity, 289
of Resistance, B.A., 141
of Resistance, British Associa-
tion, 141
of Resistance, Legal, 140
of Resistiiuce, Siemens', 142
of Resistance, B. A. and Legal,
Compared, 142
Units, Selection of. Suitable on
Squared Paper, 32
VTALUES in Amperes of Deflec-
' tions of Tangent Galvano-
meter Controlled Only by
Earth's Magnetism, 55
Variable Resistance in Voltmeters
caused by Self-induction
■ with Alternating Potential
Differences, 427
Variation of Capacity of Condenser
with Area of, and Distance
between, its Coatii^s, 303
of External Resistance, Cur-
rent, and Potential Dif-
ference at Battery Termi-
nals, 204
Variation of Magnetic Effect of
Bobbin with Current and
Resistance, 418
of Resistance with Length, 143
of Resistance with Material, 146
of Resistance with Sectional
Area, 146
of Resistance with Tempera-
ture, 147
of Resistance with Tempera-
ture, Law of, 152
of Sensibility of any Galvano-
meter by Altering Dia-
meter of "Wire, 22
of Sensibility of any Galvano.
meter with Length of Wire
used in "Winding, 418
of Sensibility of any Galvano-
meter by Shunting, 229
of Sensibility of Galvanometer
with its Resistance, 416
of Sensibility of Tangent Gal-
vanometer, 48
of Sensibility of Voltmeter with
Chanae of its Resistance,
407, 418
Produced in Total Current
by Shunting Portion of
Circuit, 253
with Temperature of E. M. F.
of DanieUs Cell, 211
with Temperature of E. M. F.
of Latimer Clark's Cell, 411
Varley's Accumulating Influence
Machine, 367
Varnish, Coating Insulating Stems
with SheU-lac, 267 3
How to make Insulating, note,
268
Varnishing Shade of Ordinary Gold-
Leaf Electroscope 97
Varying Potential Dirference in
Known Ratio, 278, 354
Vibration, Definition of Periodic
Time of, 291 •
Voltaic Element, 209
Voltameter cannot Measure Alter-
nating Current, 198
Copper, Description of, 6, 11.
(See also Copper Volta-
meter.)
Hoffmann's, 15
Silver, Used by Lord Rayleigh,
11, 395
Sulphuric Acid, Construction
of, 18
■ Sulphuric Acid, Description of, 6
Sulphuric Acid, Volume of Gaa
produced in, per Second,
by One Ampere, 12
INDEX.
515
Voltameter, Sulphuric Acid, Weight
of Gas produced in, per
Second, by One Ampere,
22
Zinc. (See Zinc Voltameter.)
Voltameters, Objections to usual
Mode of Constructing, 18
and Galvanometers, Relative
Advantages of, 20
Direction of Current in Acid,
Copper, and Zinc, 15
Disadvantage of, 20
Independence of Gas Generated
and of Metal Deposited of
Shape, Size, and Distance
Apart of Plates, 10
Precautions in Using, note, 11
Silver, note, 11
Silver, Use of, in Calibrating
Ammeters, 395—400
Weights of Metals Deposited
on Plates of, per Second,
by One Ampere, 11
Why Only Used in Measuring
Large Currents, 20
Volt, The, 86
Practical Definition of the,
141
Provisional Definition of the, 89
Voltmeters, 128, 376
Voltmeter, Cardew's Latest Form
of, 423
Cardew's, Advantages of, 426
Cardew's, Arranged for Measur-
ing Large Potential Dif-
ferences, 425
Cardew's, Diameter of Wire
Used in, 423
Cardew's, Disadvantage of, 427
Cardew's, Length of Wire Used
in Latest Form of, 423
Cardew's, No Heating Error
in, 426
Cardew's, Self-induction Small
iii, 427
Commutator, 427
Commutator, Calibrating, 433
Cunynghame's, 382
Cunynghame's, Advantages and
Disadvantages of, 385
— — Cunynghame's, Graduation of,
385
Electro-Magnetic Control, 392
Electro- Magnetic Control,
Crompton and Kapp's, 392
— Electro- Magnetic Control,
Paterson and Cooper's,
393
— Electro-Magnetic Control, Ad-
vantage and Disadvantage
of, 894
■ Gravity Control, 391
Voltmeterv Gravity Control, Ad-
vantages of, 391
Gravity Control, Disadvantages
of, 394
Magnifying Spring, 386
Magnifying SprmEr, Adjust-
ment for Seusibility in, 389
Magnifying Spring, Advantages
of, 390
Magnifying Spring, Best Law
of Gauge of W ire for Coils
of, 421
Magnifying Spring, Disadvan-
tage of, 391
Magnifying Spring, Indication
of Direction of Current in,
389
Permanent Magnet, 69
Permanent Magnet, Advantages
of, 78
Permanent Magnet, Defect of,
376
Permanent Magnet, Direct-
Reading, 76
Spring Control, 377
Standard, 422
with Magnifying Gearing, 386
Best Material for Coils of, 420
Best Material for Coils of Ex-
tei-nal Resistance for, 422
I Best- Law of Gauge of Wire
' for, 421
Calibrating by Comparison with
Standard Cell, 410
Calibrating, by Poggendorffs
Method, 413
Calibrating, with Known Cur«
rent and Resistance, 408
Errors in, 407
with External Resistance, 421
Waste of Energy in, with High
External Resistance, 422
Testing. 407
Testing, for Accuracy ot Gradu-
ation, 408
Testing, for Heating Error, 4l5
Variation of Sensibility of, with
Change of its Resistance,
407, 418
Variation of Sensibility of, with
External Resistance, 421
Variation of Sensibility of, with
Speed of Alternation of
Potential Difference, 427
Volume of Gas Produced per
Second in Sulphuric Acid
Voltameter by One Am-
pere, 12
Voss' Accumulating Influence Miw
chine, 367
Vulcanised Indiarubber, Hooper's,
Kesistaaic© of, 271
516
PRACTICAL ELECTRICITY.
w
TyASTE of Energy in Voltmeters
*' with High External Re-
sistance, 422
of Energy in Frictional Elec-
trical Machines, 352
Water, Current of, in Pipe Compared
with Electric Current, 3, 80
Difference between Pressure of,
Flowing in a Pipe, and
Electric Potential, 81
- — Equivalent, Definition of, 198
Jacket, Use of, 193
Watt, Definition of the, 442
Work done in One Minute and
One Second, when One, is
Developed, 443
Wattmeter, Construction of, 444
Errors in, 4i5
Wax, Coating Insulating Stems with
Paraffin, 267. (See also
Paraffin.)
Weighing, Measuring Potential Dif-
ference by, 88
Weight Electrometer, 88
- — Electrometer, Increasing Sen-
sibility of, by using Aux-
iliary High Potential, 91
of Gas Produced per Second,
in Sulphuric Acid Volta-
meter, by One Ampere, 12
Wheatstone's Bridge or Balance, 166
Bridge, Arms of, 172
Bridge, Best Arrangement of
Battery and Galvanometer
with, 171, 467
Bridge, Best Resistance for
Arms of, 171
Bridge, Commercial Form of,
172
Bridge, Conditions Affecting
Sensibility of, 171
Bridge Galvanometer, Best Re-
sistance for, 172, 466
Bridge Galvanometer, Current
through, 465
Bridge GsJvanometer, Meaning
of Deflection of, 176
• Bridge, Mode of Increasing
Sensibility of, 168
Bridge, Key for, 174
Bridge, Superiority of, over
Differential Galvanometer,
171
Bridge, Use of Shunt with, 176
Wiedemann and Franz's Table of
Heat Conductivities of
Metals, 159
Wimshurst Influence Machine, 367
Influence Machine, Attaching
Leyden Jars to Collectors
of, 370
Influence Machine, Collecting
Combs of, 369
Influence Machine, Work done
by, 371
Winding Resistance Coils, Mode of,
163
Windings, Variation of Sensibility
of a Galvanometer with
Number of, 48
Wire and Liquid Resistances, Com-
parison of, 194
Best Gauge of, for Differential
Galvanometer, 436
Best Gauge of, for Galvano-
meter in Simple Circuit, 435
Best Gauge of, for Galvano-
meter of Wheatstone's
Bridge, 172, 466
Wires Joined in Parallel, 136
Joined in Series, 140
Work done by Current Generator,
202
done by Wimshurst Influence
Machine, 371
done in Electric Circuit, 199
done per Minute, and per
Second, when One Watt is
Developed, 443
VAMBONI'S Construction of Dry
^ Pile, 373
Zero Instrument, Definition of, 380
Zinc Amalgam, 218
How to Amalgamate, 218
Resistance of, for Given Length
and Diameter, and for
Given Length and Weight,
157
Resistance of, per Cubic Centi-
metre, and per Cubic Inch,
154
Temperature Variation of Re-
sistance of, 160
Voltameter, Direction of Cur-
rent in, 15
Voltameter, Weight of Zinc
Deposited on Plate of, per
Second, by one Ampere, 11
PfilSTKD BY CASSELL & COMPANY, LIMITED, LA BELLE SAtTVAGE, LONDOH, ■.C.
10,191
Selections from Cassell # Company's Publications.
Jlluatratctr, ftttc-^rt, atttr ntljer !ff0lumea.
Abbeys and Churches of England and Wales, The : Descriptive,
Historical, Pictorial. In Two Vols,, 21s. each.
Adventure, The World of. Fully Illustrated. Vols. I. and II. gs. each.
American Library of Fiction. Crown 8vo, cloth, 3s. 6d. each.
A Latin-Quarter Courtship. By
Henry Harland (Sidney
Luska).
Grandison Mather. By Henry
Harland (Sidney Luska).
Her
The Tragedy of Brinkwater. By Martha
L. Moodey.
Karmel the Scout. By Sylvanus Cobb,
Junr.
Another's Crime. By Julian Hawthorne.
By Edgar Henry
American Yachts and Yachting. Illustrated. 6s.
Arabian Nights Entertainments, Cassell's Pictorial. los. 6d.
Architectural Drawing. By Phf.nM: Spiers. Illustrated. los. 6d.
Art, The Magazine of. Yearly Vol. With 12 Photogravures, Etchings,
&c., and several hundred choice Engravings. i6s.
BashkirtsefF, Marie, The Journal of. Cheap Edition. 7s. 6d.
Library Edition, in Two Vols.. 24s.
Birds' Nests, Eggs, and Egg-Collecting. By R. Kearton. Illus-
trated with 16 Coloured Plates. 5s.
Black Arrow, The. A Tale of the Two Roses. By R. L. Stevenson. 5s.
British Ballads. With 275 Original Illustrations. Two Vols. 7s. 6d. each.
British Battles on Land and Sea. By James Grant. With about
600 Illustrations. Three Vols., 4to, £l 7s.; Library Edition, £1 los.
British Battles, Recent. Illustrated. 4to, gs. ; Library Edition, los.
British Empire, The. By Sir George Campbell, M.P. 3s.
Browning, An Introduction to the Study of. By A. Svmons. as. 6d.
Bunyan's Pilgrim's Progress and The Holy War, Cassell's Illus-
trated Edition of. With 2co Original Illustrations. Demy 4to,
cloth, i6s.
Butterflies and Moths, European. With 61 Coloured Plates. 35s.
Canaries and Cage-Birds, The Illustrated Book of. With 56 Fac-
simile Coloured Plates, 35s. Half-morocco, £2 5s.
Cannibals and Convicts. By Julian Thomas (" The Vagabond"). 5s.
Captain Trafalgar. By Westall and Laurie. 5s.
Cassell's Family Magazine. Yearly Vol. Illustrated, gs.
Celebrities of the Century. Cheap Edition. los. 6d,
Choice Dishes at Small Cost. By A. G. Payne, is.
Cities of the World. Four Vols. Illustrated. 7s. 6d. each.
Civil Service, Guide to Employment in the. 3s. 6d.
Civil Service. — Guide to Female Employment in Government
Offices. IS.
Climate and Health Resorts. By Dr. Burney Yeo. New and
Cheaper Edition. 7s. 6d.
Clinical Manuals for Practitioners and Students of Medicine. A
List of Volumes forwarded post free on application to the Publishers,
Clothing, The Influence of, on Health. By F. Treves, F.R C.S. 2s.
Colonists, Medical Handbook for. By E. A. Barton, M.R.C.S. 2s.6d.
Colour. By Prof. A. H. Church. With Coloured Plates. 3s. 6d.
Columbus, Christopher. By Washington Irving. Three Vols. 7s. 6d.
Commerce, The Year- Book of. Second Year's Issue. 5s.
Commodore Junk. By G. Manville Fenn. 53.
Conquests of the Cross. With numerous Illustrations. Vol. I., gs.
Cookery, A Year's. By Phyllis Browne. 3s. 6d.
Cookery, Cassell's Dictionary of. Containing about Nine Thousand
Recipes. 7s. 6d. ; Roxburgh, los. 6d.
Cookery, CasseH's Popular. With Four Coloured Plates. Cloth gilt, as.
Cookery, Cassell's Shilling. 384 pages, limp cloth, xs.
S c 8.90
Selections from Cassell i' Company's Publications,
Copyright, The Law of Musical and Dramatic. By Edward
Cutler, Thomas Eustace Smith, and Frederick E. Wbatherly,
Esquires, Barristers-at-Law. 3s. 6d.
Countries of the World, The. By Robert Brown, M.A., Ph.D., &c.
Complete in Six Vols., with about 750 Illustrations. 4to, 7s. 6d. each.
Cromwell, Oliver. By J. Allanson Picton, M.P. 53.
Culmshire Folk. By the Author of " John Orlebar," &c. 3s. 6d.
Cyclopaedia, Cassell's Concise. With 12,000 subjects, brought down
to the latest date. With about 600 Illustrations. Cheap Edition. 7s. 6d.
Cyclopaedia, Cassell's Miniature. Containing 30,000 subjects. 3s. 6d.
Dairy Farming. By Prof. J. P. Sheldon. With 25 Coloured Plates. 21s.
David Todd: The Romance of his Life and Loving. By David
Maclure. 5s.
Dead Man's Rock. A Romance. By Q. 5s.
Dickens, Character Sketches from. First, Second, and Third Series.
With Six Original Drawings in each by F. Barnard. In Portfolio,
21 s. each.
Dog, Illustrated Book of the. By Vero Shaw, B.A. With 28 Coloured
Plates. Cloth bevelled, 35s. ; half- morocco, 45s.
Dog, The. By Idstone. Illustrated. 2s. 6d.
Domestic Dictionary, The. Illustrated. Cloth, 7s. 6d.
Dor^ Gallery, The. With 250 Illustrations by Dor6. 4to, 42s.
Dore's Dante's Inferno. Illustrated by Gustave Dor6. 21s.
Dor6's Dante's Purgatorio and Paradiso. Illustrated by Dor6. 2IS.
Dore's Milton's Paradise Lost. Illustrated by Dor6. 4to, 21s.
Earth, Our, and its Story. By Dr. Robert Brown, F.L.S. With
Coloured Plates and numerous Wood Engravings. Three Vols. gs. each.
Edinbureh, Old and New. With 600 Illustrations. Three Vols. qs. each.
Egypt: Descriptive, Historical, and Picturesque. By Prof. G. Ebers.
With 800 Original Engravings. Popular Edition. In Two Vols, 42s.
Electricity in the Service of Man. With nearly 850 Illustrations.
Cheap Edition. Price gs.
Electricity, Age of. By Park Benjamin, Ph.D. 78. 6d.
Electricity, Practical. By Prof. W. E. Ayrton. 7s. 6d.
Encyclopaedic Dictionary, The. A New and Original Work of Refer-
ence to all the Words in the English Language. Complete in Fourteen
Divisional Vols., los. 6d. each; or Seven Vols., half-morocco, 2is.
each ; half-russia, 25s.
England, Cassell's Illustrated History of. With 2,000 Illustrations.
Ten Vols., 4to, gs. each. Revised Edition. Vols. I., II.. and III.,
g*:. each.
English History, The Dictionary of. Cheap Edition. los. 6d.
•English Literature, Dictionary of. By W. Davenport Adams.
Cheap Edition, 7s. 6d. ; Roxburgh, los. 6d.
English Literature, Library of. By Prof. Henry MdRLEY,
Vol. 1.— Shorter English Poems. 7s. 6d.
Vol. II. — Illustrations of English Religion. 7s. 6d.
Vol. III. — English Plays. 7s. 6d.
Vol. IV.— Shorter Works in English Prose. 7s. 6d.
Vol. v.— Sketches of Longer Works in English Verse and
Prose. 7s. 6d.
English Literature, Morley's First Sketch of. Revised Edition, ys.bd.
English Literature, The Story of. By Anna Buckland. 3s. 6d.
English Writers. By Prof. Henry Morley. Vols. I. to V. 5s. each.
/Esop's Fables. Illustrated by Ernest Griset. Cloth, 3s. 6d.
Etching. By S. K. Koehler. With 30 Full-Page Plates. £4 4s.
Etiquette of Good Society, xs. ; cloth, is. 6d.
Europe, Pocket Guide to, Cassell's. Leather, 6s.
Eye, Ear, and Throat, The Management of the. 3s. 6d.
Selections from Casseil ^ Company's Publications.
Family Physician, The. By Eminent Physicians and Surgeons.
New and Revised Edition. Cloth, 3is. ; Roxburgh, 35s.
Fenn, G. Manville, Works by. Boards, as. each ; cloth, as. 6d. each.
My Patients. Being the Notes
of a Navy Surgeon.
Dutch the Diver.
The Parson o' Dumford.
The Vicar's People. ) in cloth
Sweet Mace. j only.
Poverty Corner.
Field Naturalist's Handbook, The. By the Rev. J. G. Wood
and Rev. Theodore Wood. 5s.
Figuier's Popular Scientific Works. With Several Hundred Illustra-
tions in each. 3s. 6d. each.
The Human Race. I The Insect World.
Reptiles and Birds. | Mammalia.
Fine-Art Library, The. Edited by John Sparkes, Principal of the
South Kensington Art Schools. Each Book contains about 100
Illustrations. 5s. each.
Engraving.
Tapestry.
The English School of Paint-
ing.
The Flemish School of Paint-
ing.
The Education of the Artist.
(Non-illustrated.)
Greek Archaeology.
Artistic Anatomy.
The Dutch School of Painting.
Flower Painting in Water Colours. With Coloured Plates. First
and Second Series. 5s. each.
Flower Painting, Elementary. With Eight Coloured Plates. 3s.
Flowers, and How to Paint Them. By Maud Nafteu With
Coloured Plates. 5s.
Forging of the Anchor, The. A Poem. By Sir Samuel Ferguson,
LL.D. With 20 Original Illustrations, Gilt edges, 5s.
Fossil Reptiles, A History of British. By Sir Richard Owen,
K.C.B., F.R.S., &c. With 268 Plates. In Four Vols., £ia X2s.
France as It Is. By Andr6 X.ebon and Paul Pelet. With Three
Maps. Crown 8vo, cloth, 7s. 6d.
Garden Flowers, Familiar. By Shirley Hibberd. With Coloured
Plates by F. E. Hulme, F.L.S. Complete in Five Series. 12s. 6d. each.
Gardening, Cassell's Popular. Illustrated. 4 vols., 5s. each.
Gas, The Art of Cooking by. By Marie Jenny Sugg. Illustrated.
Cloth, 38. 6d.
Gaudeamus. One Hundred Songs for Schools and Colleges. Edited by
John Farmer, 5s.
Geometrical Drawing for Army Candidates. By H. T. Lilley,
M.A. as.
Geometry, First Elements of Experimental. By Paul Bert. is. 6d.
Geometry, Practical Solid. By Major Ross. as.
Gleanings from Popular Authors. Two Vols. With Original Illus-
trations. 4to, gs, each. Two Vols, in One, 15s.
Great Painters of Christendom, The, from Cimabue to Wilkie.
By J©HN Forbes-Robertson. Illustrated throughout. 12s. 6d.
Gulliver's Travels. With 88 Engravings by Morten. Cheap Edition,
Cloth, 5s. 6d. ; cloth gilt, 5s.
Gun and its Development, The. By W. W. Greener. With 500
Illustrations. los. 6d.
Guns, Modern Shot. By W, W. Greener. Illustrated, 5s.
Health at School. By Clement Dukes, M,D., B.S. 7s. 6d.
Health, The Book of. By Eminent Physicians and Surgeons. Cloth,
21 s. ; Roxburgh, 25s.
Health, The Influence of Clothing on. By F. Treves, F.R,G.S. as.
Heavens, The Story of the. By Sir Robert Stawell Ball, LL.D.,
F.R.S,, F.R.A.S. With Coloured Plates. Popular Edition. 12s. 6d.
Selections from Cassell ^ Company's Publications.
Heroes of Britain in Peace and War. In Two Vols., with 300
Original Illustrations. 5s. each ; or One Vol., library binding, 10s. 6d.
Holiday Studies of Wordsworth. By Rev. F. A. Malleson, M.A. 5s.
Homes, Our, and How to Make them Healthy. By Eminent
Authorities. Illustrated. 15s.
Horse, The Book of the. By Samuel Sidney. With 28 Fac-simile
Coloured Plates. Enlarged Edition. Demy 410, 35s.; half-morocco, 45s.
Houghton, Lord : The Life, Letters, and Friendships of Richard
Monckton Milnes, First Lord Houghton. By T. Wemvss
Reid. In Two Vols., with Two Portraits. 32s.
Household, Cassell's Book of the. Vols. I., II., and III., 5s. each.
Household Guide, Cassell's. Illustrated. Four Vols., 20s.
How Women may Earn a Living. By Mercy Grogan. 6d.
India, Cassell's History of. By James Grant. With about 400
Illustrations. Library binding. One Vol. iss.
Irish Union, The; Before and After. By A. K. Connell, M.A. 2s.6d.
"Japanese " Library. Consisting of Twelve Popular Works, printed on
thin paper, is. 3d. each nett.
Handy Andy. — Oliver Twist. — Ivanhoe. — Ingoldsby Legends.—
The Last of the Mohicans. — The Last Days of Pompeii— The
Yellowplush Papers. — The Last Days of Palmyra. — Jack
Hinton, the Guardsman. — Selections from Hood's Works.—
American Hum.ovu:.— The Tower of London.
John Orlebar, Clk. By the Author of '* Culmshire Folk." 2s.
John Parmelee's Curse. By Julian Hawthorne. 2s. 6d.
Karmel the Scout. A Novel. By Svlvanus Cobb, Junr. Cloth, 3s. 6d.
Kennel Guide, The Practical. By Dr. Gordon Stables, is.
Khiva, A Ride to. By Col. Fred. Burnaby. is. 6d.
Kidnapped. By R. L. Stevenson. Illustrated Edition. 5s.
King Solomon's Mines. By H. Rider Haggard. Illustrated Edition. 5%.
Ladies' Physician, The. A Guide for Women in the Treatment of
their Ailments. By a Physician. 6s.
Lady Biddy Fane, The Admirable. By Frank Barrett. 5s.
Lake Dwellings of Europe. By Robert Munro, M.D., M.A.
Cloth, 31s. 6d. ; Roxburgh, £2 2S.
Landscape Painting in Oils, A Course of Lessons in. By A. F.
Grace. With Nine Reproductions in Colour. Cheap Edition, 25s.
Law, How to Avoid. By A. J. Williams, M.P. is. Cheap Edition.
Legends for Lionel. By Walter Crane. Coloured Illustrations^ 5s.
Letts's Diaries and other Time-saving Publications are now pub-
lished exclusively by Cassell & Company. {A list free on application.)
Life Assurance, Medical Handbook of. By James Edward Pol-
lock, M.D., and James Chisholm. 7s. 6d.
Loans Manual. A Compilation of Tables and Rules for the Use of Local
Authorities. By Charles P. Cotton. 5s.
Local Government in England and Germany. By the Right Hon.
Sir Robert Morier, G.C.B., &c. is.
London, Greater. By Edward Walford. Two Vols. With about
400 Illustrations, gs. each.
London, Old and New. Six Vols., each containing about 200
Illustrations and Maps. Cloth, gs. each.
London Street Arabs. By Mrs. H. M. Stanley (Dorothy Tennant).
A Collection of Pictures. Descriptive Text by the Artist. 5s.
Longfellow's Poetical Works. Illustrated, £3 3s.; Popular Editton,x&s.
Magic at Home. By Prof. Hoffman. Fully Illustrated. 5s.
Master of Ballantrae, The. By Robert Louis Stevenson. 5s.
Mathew, Life cf Father. By F.J. Mathew, a Grand-nephew. 2s 6d.
Selections from Cassell # Company's Publications.
Mechanics, The Practical Dictionary of. Containing 15,000 Draw-
ings. Four Vols. 21S. each.
Medicine, Manuals for Students of. [A List fonvarded post free.)
Metropolitan Year-Book, The. Paper, as. ; cloth, 2s. 6d.
Metzerott, Shoemaker. Cr. 8vo, 5s.
Modern Europe, A History of. By C. A. Fvffe, M.A. Complete in
Three Vols. 12 s. each.
Music, Illustrated History of. By Emil Naumann. Edited by the
Rev. Sir F. A. Gore Ouseley, Bart. Illustrated. Two "Vols. 31s. 6d.
National Library, Cassell's. In Volumes, each containing about
192 pages. Paper covers, 3d. ; cloth, 6d. {,A Complete List 0/ the
Volumes will be sent post free on application.)
Natural History, Cassell's Concise. By E. Perceval Wright,
M.A., M.D., F.L.S. With several Hundred Illustrations. 7s. 6d.
Natural ' History, Cassell's New. Edited by Prof. P. Martin
Duncan, M.B., F.R.S., F.G.S. Complete in Six Vols. With about
2.000 Illustrations. Cloth, gs. each.
Nature's Wonder Workers. By Kate R. Lovell. Illustrated. 5s.
Nursing for the Home and for the Hospital, A Handbook of.
By Catherine J. Woou. Cheap Edition, is. 6d. ; cloth, 2s.
Nursing of Sick Children, A Handbook for the. By Catherine
J. Wood. 2s. 6d.
Oil Painting, A Manual of. By the Hon. John Collier. 2s. 6d.
Our Own Country. Six Vols. With 1,200 Illustrations. 7s. 6d. each.
Pactolus Prime. A Novel. By Albion W. Tourg6e. 5s.
Painting, Practical Guides to. With Coloured Plates and full in-
structions : —
Marine Painting. 5s.
Animal Painting. 5s.
China Painting. 5s.
Figure Painting. 7s. 6d.
Elementary Flower Paint-
ing. 3s.
Flower Painting, Two Books,
5s. each.
Tree Painting. 5s.
Water-Colour Painting. 5s.
Neutral Tint. 5s.
Sepia, in Two Vols., 3s. each ; or
in One Vol., 5s.
Flowers, and How to Paint
Them. 5s.
Paxton's Flower Garden. By Sir Joseph Paxton and Prof. Lindlev.
With 100 Coloured Plates. Price on application.
People I've Smiled with. By Marshall P. Wilder. 2s. ; cloth, 2s.6d.
Peoples of the World, The. In Six Vols. By Dr. Robert Brown.
Illustrated. 7s. 6d. each.
Phantom City, The. By W. Westall. 53.
Photography for Amateurs. By T. C. Hepworth. Illustrated, is.;
or cloth, IS. 6d.
Phrase and Fable, Dictionary of. By the Rev. Dr. Brewer. -Cheap
Edition, Enlarged, cloth, 3s. 6d. ; or with leather back, 4s. 6d.
Picturesque America. Complete in Four Vols., with 48 Exquisite Steel
Plates and about 800 Original Wood Engravings. £2 2S. each.
Picturesque Australasia, Cassell's. With upwards of 1,000 Illustrations.
Complete in Four Vols., 7s. 6d. each.
Picturesque Canada. With 600 Original Illustrations. 2 Vols. £3 3s. each.
Picturesque Europe. Complete in Five Vols. Each containing
13 Exquisite Steel Plates, from Original Drawings, and nearly 200
Original Illustrations. Original Edition. Cloth, £21 ; half-morocco,
£31105.; morocco gilt, £52 los. The Popular Edition is published in
Five Vols., i8s. each.
Picturesque Mediterranean. With Magnificent Original Illustrations
by the leading Artists of the Day. Vol. I. £2 2S.
Pigeon Keeper, The Practical. By Lewis Wright. Illustrated. 3s. 6d.
Pigeons, The Book of. By Robert Fulton. Edited and Arranged by
L. Wright. With 50 Coloured Plates, 31s. 6d. ; half-morocco, £2 2S.
Selections from Cassell ^- Company's Publications,
Poems, Aubrey de Vere's. A Selection. Edited by John Dennis.
3S. 6d.
Poets, Cassell's Miniature Library of the :
Burns. Two Vols, as. 6d.
Byron. Two Vols. 2s. 6d.
Hood. Two Vols. as. 6d.
Longfellow. Two Vols. as. 6d.
Milton. Two Vols. as. 6d.
Scott. Two Vols. as. 6d. [as. 6d.
Sheridan and Goldsmith. 2 Vols.
Wordsworth. Two Vols. as. 6d.
Shakespeare. Illustrated. In 12 Vols., in Case, las.
Police Code, and Manual of the Criminal Law. By C. E. Howard
Vincent, M.P. as.
Polytechnic Series, The.
Forty Lessons in Carpentry Workshop Practice. Cloth ^ilt, is.
Practical Plane and Solid Geometry, including Graphic Arithmetic. Vol, I.,
Elementary Stage. Cloth gilt, 3s.
Forty Lessons in Enjjineering Workshop Practice, is. 6d.
Technical Scales. Set of Ten in cloth case, is.
Elementary Chemistry for Science Schools and Classes. Crown Svo, is. 6d.
Popular Library, Cassell's. Cloth, is. each. {A Ustpost/ree on ajypli-
cation. )
Portrait Gallery, The Cabinet. Containing 36 Cabinet Photographs of
Eminent Men and Women. With Biographical Sketches. Vol. I. 15s.
Poultry Keeper, The Practical. By Lewis Wright. With Coloured
Plates and Illustrations. 3s. 6d.
Poultry, The Book of. By Lewis Wright. Popular Edition. 10s. 6d.
Poultry, The Illustrated Book of. By Lewis Wright. With Fifty
Coloured Plates. New and Revised Edition. Cloth, 31s. 6d.
Pre-Raphaelites, The Italian, in the National Gallery. By Cosmo
Monkhouse. Illustrated, is.
Queen Victoria, The Life and Times of. By Robert Wilson. Com-
plete in Two Vols. With numerous Illustrations, gs. each.
Quiver, The. Yearly Volume. Illustrated. 7s. 6d.
Rabbit- Keeper, The Practical. By Cuniculus. Illustrated. 3s. 6d.
Railway Guides, Official Illustrated. With Illustrations, Maps, &c.
Price IS. each ; or in cloth, as. each.
Great Western Railway. R eznsed and Enlarged.
Great Northern Railway,
London, Brighton and South Coast Railway.
London and North- Western Railway. Revised and Enlarged.
London and South-Western Railway.
Midland Railway.
South-Eastern Railway.
Railway Library, Cassell's. Crown Svo, boards, as. each.
Undrr a Strange Mask. By Frank
Barrett.
The coombsberrow Mystery. By
tames Colwall.
Dead Man's Rock. By Q.
A Queer Race. By W. westall.
Captain Trafalgar. By Westall
and Laurie,
the phantom City. By w. avestall.
•»• The above can also be obtained in
cloth, 2S. td. each.
Jack Gordon, knight Errant,
Gotham, 18S3. By Barclay
North.
THE Diamond Button. By Barclay
north.
Another's Crime. By Julian Haw-
thorne.
The Yoke of the Thorah. By
Sidney Luska.
Who is John noman? By Charles
HENRY Beckett.
The Tragedy of Brinkwater, By
Martha l. moodey,
AN American Penman. By Julian
Hawthorne.
Section 558; or, The Fatal Letter.
By JULIAN Hawthorne.
The Brown Stone boy. By W. H.
Bishop.
A Tragic Mystery. By Julian
Hawthorne.
The Great Bank Robbery. By
JULIAN Hawthorne.
Richard, Henry, M.P. A Biography. By Charles S. Miall. 7s. 6d.
Rivers of Great Britain, The : Descriptive, Historical, Pictorial.
Rivers of the East Coast. 42s.
Selections from Cassell # Company's Publications,
Rossetti, Dante Gabriel, as Designer and Writer. Notes by
William Michael Rosshtti. 7s. 6d.
Royal River, The : The Thames, from Source to Sea. With Descrip-
tive Text and a Series of beautiful Engravings. £2 2s.
Russia. By Sir Donald Mackenzie Wallace, M.A. 5s.
Russo-Turkish War, Cassell's History of. With about 500 Illus-
trations. Two Vols., gs. each.
Red Library, Cassell's. Stiff covers, is. each; cloth, 2s. each.
The Antiquary.
Nicholas Nickleby
(Two Vols.).
Jane Eyre.
"Wuthering Heights.
Dombey and Son
( Two Vols.).
The Prairie.
Night and Morning.
Keuilworth.
The Ingoldsby Le-
gends,
The Tower of
London.
The Pioneers.
Charles O'MaUey.
Barnaby Rudge.
Cakes and Ale.
The King's Own.
People I have Met.
The Pathfinder.
Evelina.
Seott'o Poems.
Last of the Barons.
Adventures of Mr.
Ledbury.
Ivanhoe.
Oliver Twist.
Selections from Hood's
"Works.
Longfellow's Prose
Works.
Sense and Sensibility.
Lytton's Plays.
Tales, Poems, and
Sketches. Bret Harte.
Martin Chuzzlewit
(Two Vols.).
The Prince of the
House of David.
Sheridan's Plays.
Uncle Tom's Cabin.
Deerslayer.
Eugene Aram.
Home and the Early
Christians.
The Trials of Mar-
garet Lyndsay.
Jack Hinton.
Poe's Works.
Old Mortahty.
The Hour and the Man.
Handy A ndy.
Scarlet Letter,
Pickwick (Two Vols.).
Last of the Mohicans.
Pride and Prejudice.
yellowplush Papers.
Tales of the Borders.
Last Days of Palmyra.
Washington Irving's
Sketch-Book.
The Talisman.
Rienzi.
Old Curiosity Shop.
Heart of Midlothian.
Last Days of Pompeii.
American Humour,
I Sketches by Boz,
Macaulay's Lays and
i Essays,
I Harry Lorrequer,
St. Cuthbert's Tower, By Florence Warden, Cheap Edition. 58.
Saturday Journal, Cassell's. Yearly Volume, cloth, 7s. 6d.
Science for All, Edited by Dr. Robert Brown. Revised Edition.
Illustrated, Five Vols, gs. each.
Sculpture, A Primerof. By E.Roscok Mullins. With Illustrations, 2s.6d.
Sea, The: Its Stirring Story of Adventure, Peril, and Heroism.
By F. Whymper, With 400 Illustrations. Four Vols,, 7s. 6d. each.
Secret of the Lamas, The. A Tale of Thibet. Crown 8vo, 5s.
Shaftesbury, The Seventh Earl of, K,G., The Life and Work of. By
Edwin Hodder. Three Vols,, 36s, Popular Edition, One Vol., 7s, 6d.
Shakespeare, The Plays of. Edited by Professor Henry Morley,
Complete in 13 Vols,, cloth, 21s,
Shakespeare, Cassell's Quarto Edition. Containing about 600 Illus-
trations by H, C, Selous. Complete in Three Vols,, cloth gilt, £3 3s.
Shakespeare, Miniature. Illustrated. In Twelve Vols., in box, 12s. ;
or in Red Paste Grain (box to match), with spring catch, ais.
Shakespeare, The England of. By E. Goadby, Illustrated. 2s, 6d.
Shakspere, The International. Edition de Luxe.
"OTHELLO," Illastrated by Frank DiCKSEE, A.R.A. £3105.
" KING HENRV IV." Illustrated by Eduard Gkutzner, £3 ids.
"AS YOU LIKE IT." Illustrated by Emile Bayaru, £3 ios,
"ROMEO AND JULIET," Illustrated by F, Dicksee, A.R.A,, £555.
Shakspere, The Leopold. With 400 Illustrations. Cheap Edition.
3S. 6d. Cloth gilt, 6s. ; Roxburgh, 7s. 6d.
Shakspere, The Royal. With Steel Plates and Wood Engravings.
Three Vols. 15s. each.
Sketching from Nature in Water Colours. By Aaron Penley.
With Illustrations in Chromo-Lithography. 15s.
Social Welfare, Subjects of. By Sir Lyon Playfair, K.C.B. 7s. 6d
Socialism, Lectures on Christianity and. By Bishop Barry. 3s. 6d.
Splendid Spur, The. Edited by Q. 5s.
Selections front Cassell ^ Company's Publications.
Sports and Pastimes, Cassell's Complete Book of. Cheap Edition.
With more than 900 Illustrations. Medium 8vo, Q92 pages, cloth, 3s. 6d.
Stanley in East Africa, Scouting for : a Record of the Adventures
of Thomas Stevens in Search of H. M. Stanley. With 14 Illus-
trations. Cloth, 7s. 6d.
Star-Land. By Sir Robert Stawell Ball, LL.D., F.R.S., F.R.A.S.
Illustrated. Crown 8vo, 6s.
Steam Engine, The. By W. H. Northcott, C.E. 3s. 6d.
Strange Doings in Strange Places. Complete Sensational Stories by
Frank Barrett, Q, G. Manvillk Fenn, &c. &c. Cr. 8vo, 5s.
Technical Education. By F. C. Montague. 6d.
Thackeray, Character Sketches from. Six New and Original Draw-
ings by Frederick Barnard, reproduced in Photogravure. 21s.
Treasure Island. By R. L. Stevenson. Illustrated. 5s.
Treatment, The Year- Book of. A Critical Review for Practitioners of
Medicine and Surgery. Greatly Enlarged. 500 pages. 7s. 6d.
Trees, Familiar. By G. S. Boulger, F.L.S. Two Series. With 40
full-page Coloured Plates by W. H. J, Boot. 12s. 6d. each.
Troy Town, The Astonishing History of. By Q. 5s.
Two Women or One ? From the Manuscripts of Doctor Leonard
Benary. By Henry Harland. is.
••Unicode": the Universal Telegraphic Phrase Book. Desk or
Pocket Edition. 2s. 6d.
United States, Cassell's History of the. By the late Edmund
Ollier. With 600 Illustrations. Three Vols. gs. each.
United States, Youth's History of the. Illustrated. 4 Volumes. 36s.
Universal History, Cassell's Illustrated. Four Vols. gs. each.
Verdict, The. A Tract on the Political Significance of the Report of the
Parnell Commission. By Prof. A. V. Dicey, Q.C. 2s. 6d.
Vicar of 'Wakefield and other Works by Oliver Goldsmith.
Illustrated. 3s. 6d. ; cloth, gilt edges, 5s.
W^hat Girls Can Do. By Phyllis Browne. 2s. 6d.
Wild Birds, Familiar. By W. Swaysland. Four Series. With 40
Coloured Plates in each. 12s. 6d. each.
Wild Flowers, Familiar. By F. E. Hulme, F.L.S., F.S.A. Five
Series. With 40 Coloured Plates in each. I2s. 6d. each.
Woman's World, The. Yearly Volume. i8s.
Wood, Rev. J. G., Life of the. By the Rev. Theodore Wood.
Demy Svo, cloth, price los. 6d.
Work. An Illustrated Magazine of Practice and Theory for all Work-
men, Professional and Amateur. Yearly Vol., 7s. 6d.
World of Wit and Humour, The. With 400 Illustrations. Cloth,
7s. 6d. ; cloth gilt, gilt edges, los. 6d.
World of Wonders. Two Vols. With 400 Illustrations. 7s. 6d. each.
Yule Tide. Cassell's Christmas Annual, is.
ILLUSTRATED MAGAZINES.
The Quiver. Enlarged Series. Monthly, 6d.
Cassell's Family Magazine, Monthly, 7d.
** lAttle Folks" Magazine. Monthly, 6a.
The Magazine of Art. Monthly, is.
CasselVs Saturday ,Tournal. Weekly, id. ; Monthly, 6d.
Work. Weekly, id. ; Monthly, 6d.
Catalogues of Cassell & Company's publications, which may be had at all '
Booksellers', or will be sent post free on application to the Publishers :—
Cassell's Complete Catalogue, containing particulars of upwards of
One Thousand Volumes.
Cassell's classified Catalogue, in which their Works are arranged
according to price, from Threepence to Fifty Guineas.
CASSELL'S Educational Catalogue, containing particulars of Cas ^eli,
& company's Educational Works and Students' Manuals.
CASSELL & COMPANY, Limited, Ludgate Hill, London.
Selections from Cassell # Company s Publications.
gibka antr fl£lt0:oujs Utorka.
Bible, Cassell's Illustrated Family. With 900 Illustrations. Leather,
gilt edges, £2 los.
Bible Dictionary, Cassell's. With nearly 600 Illustrations. 7s. 6d.
Bible Educator, The. Edited by the Very Rev. Dean Plumptre, D.D.,
Wells. With Illustrations, Maps, &c. Four Vols., cloth, 6s. each.
Bible Student in the British Museum, The. By the Rev. J. G.
KiTCHIN, M.A. is.
Biblewomen and Nurses. Yearly Volume. Illustrated. 3s.
Bunyan's Pilgrim's Progress (Cassell's Illustrated). 4to. 7s. 6d.
Bunyan's Pilgrim's Progress. With Illustrations. Cloth, 3s. 6d.
Child's Bible, The. With 200 Illustrations. 150^;^ Thousand. 7s. 6d.
Child's Life of Christ, The. With 200 Illustrations. 7s. 6d.
"Come, ye Children." Illustrated. By Rev. Benjamin Waugh. 5s.
Dore Bible. With 238 Illustrations by Gustave Dor6. Small folio,
cloth, £8 ; best morocco, gilt edges, £15.
Early Days of Christianity, The. By the Ven. Archdeacon Farrar,
D.D., F.R.S.
Library Edition. Two Vols., 24s. ; morocco, £2 2s.
Popular Edition. Complete in One Volume, cloth, 6s. ; cloth, gilt
edges, 7s. 6d. ; Persian morocco, los. 6d. ; tree-calf, 15s.
Family Prayer-Book, The. Edited by Rev. Canon Garbett, M.A.,
and Rev. S. Martin. Extra crown 4to, cloth, 5s. ; morocco, i8s.
Glories of the Man of Sorrows, The. Sermons preached at St. James's,
Piccadilly. By Rev. H. G. Bonavia Hunt, Mus.D., F.R.S., Ed. as. 6d.
"Heart Chords." A Series of Works by" Eminent Divines. Bound in
cloth, red edges. One Shilling each.
MV Bible. By the Right Rev. W. BOYD
Carpenter, Bishop of Ripon.
MY Father. By the Right Rev. ASH-
TON OXENDEN, late Bishop of Mon-
treal.
My work for God. By the Right
Rev. Bishop COTTERILL.
MY OBJECT IN LIFE. By the Ven.
Archdeacon Farrar, D.D.
My Aspirations. By the Rev. G.
Matheson, D.D.
MY EMOTIONAL LIFE. By the Rev.
Preb. CHADWICK, D.D.
MY BODY. By the Rev. Prot W. G.
BLAIKIE, D.D.
MY Growth in Divine Life. By the
Rev. Preb. REYNOLDS, M.A.
MY SOUL. By the Rev. P. B. POWER,
M.A.
MY Hereafter. By the Very Rev.
Dean Bickersteth.
My Walk with god. By the Very
Rev. Dean Montgomery.
My Aids to the divine Life. By
the Very Rev. Dean BOVLE.
MY SOURCES OF STRENGTH. By the
Rev. E.E.JENKINS, M.A., Secretary
of Wesleyan Missionary Society.
Helps to Belief. A Series of Helpful Manuals on the Religious
Difficulties of the Day. Edited by the Rev. Teignmouth Shore, M.A.,
Chaplain-in-Ordinary to the Queen. Cloth, is. each.
Miracles. By the Rev. Brownlow
Maitland, M.A.
Creation. By the Lord Bishop of
Carlisle.
The Divinity of Our Lord. By
the Lord Bishop of Derry.
The Morality of the Old Testa-
ment. By the Rev. Newman
Smyth. D.D.
PRAYER. By the Rev. T. Teignmouth
Shore, M.A.
The Atonement. By the Lord Bishop
of Peterborough.
Holy Land and the Bible, The. By the Rev. Cunningham Ghikie,
D.D. Two Vols., with Map, 24s.
" I Must." Short Missionary Bible Readings. By Sophia M. Nugent.
Enamelled covers, 6d. ; cloth, gilt edges, is.
S B. 8.90
Selections from Cassell ^ Company's Publications.
Life of Christ, The. By the Ven. Archdeacon Farrar, D.D., F.R.S.
Illustrated Edition, whh about 300 Original Illustrations.
Extra crown 410, cloth, gilt edges, 2is. ; morocco antique, 42s.
Library Edition. Two Vols. Cloth, 24s. ; morocco, 42s.
Popular Edition, in One Vol. 8vo, cloth, 6s. ; cloth, gilt edges,
7s. 6d. ; Persian morocco, gilt edges, los. 6d. ; tree-calf, 15s.
Marriage Ring, The. By William Landels, D.D. New and
Cheaper Edition. 3s. 6d.
Moses and Geology ; or, The Harmony of the Bible with Science.
By the Rev. Samuel Kinns, Ph.D., F.R.A.S. Illustrated. Chea.p
Eiiition, 6s.
New Testament Commentary for English Readers, The. Edited
by the Rt. Rev. C. J. Ellicott, D.D., Lord Bishop of Gloucester
and Bristol. In Three Volumes, 2is. each.
Vol. I.— The Four Gospels.
Vol. II. — The Acts, Romans, Corinthians, Galatians.
Vol. III. — The remaining Books of the New Testament.
New Testament Commentary. Edited by Bishop Ellicott. Handy
Volume Edition. St. Matthew, 3s. 6d. St. Mark, 3s. St. Luke,
3s. 6d. St. John, 3s. 6d. The Acts of the Apostles, 3s. 6d. Romans,
2S. 6d. Corinthians I. and II., 3s. Galatians, Ephesians, and Philip-
pians, 3s. Colossians, Thessalonians, and Timothy, 3s. Titus,
Philemon, Hebrews, and James, 3s. Peter, Jude, and John, 3s.
The Revelation, 3s. An Introduction to the New Testament, 3s. 6d.
Old Testament Commentary for English Readers, The. Edited
by the Right Rev. C. J. Ellicott, D.D., Lord Bishop of Gloucester
and Bristol. Complete in 5 Vols., 2is. each.
Vol. I.— Genesis to Numbers. I Vol. III.— Kings I. to Esther.
Vol.11. — Deuteronomy to Vol. IV. — Job to Isaiah.
Samuel II. | Vol. V. —Jeremiah to Malachi.
Old Testament Commentary. Edited by Bishop Ellicott. Handy
Volume Edition. Genesis, 3s. 6d. Exodus, 3s. Leviticus, 3s.
Numbers, 2s. 6d. Deuteronomy, 2s. 6d.
Protestantism, The History of. By the Rev. J. A. Wylie, LL.D.
Containing upwards of 600 Original Illustrations. Three Vols., gs. eaclj.
Quiver Yearly Volume, The. 250 high-class Illustrations. 7s. 6d.
Religion, The Dictionary of. By the Rev. W. Benham, B.D. 2IS. ;
Roxburgh, 25s.
St. George for England ; and other Sermons preached to Children. By
the Rev. T. Teignmouth Shore, M.A. 5s.
St. Paul, The Life and Work of. By the Ven. Archdeacon Farrar,
D.D., F.R.S., Chaplain-in-Ordinary to the Queen.
Library Edition. Two Vols., cloth, 24s. ; calf, 42s.
Illustrated' Edition, complete in One Volume, with about 300
Illustrations, ^x is. ; morocco, £2 2S.
Popular Edition. One Volume, 8vo, cloth, 6s. ; cloth, gilt edges,
7s. 6d. ; Persian morocco, los. 6d. ; tree-calf, 15s.
Secular Life, The Gospel of the. Sermons preached at Oxford. By
the Hon. Canon Fre.mantle. Cheaper Edition, is. 6d.
Shall We Know One Another in Heaven ? By the Rt. Rev. J. C.
Ryle, D.D., Bishop of Liverpool. Cheap Edition. Paper covers, 6d.
Stromata. By the Ven. Archdeacon Shrringham, M.A. 2s. 6d.
"Sunday," Its Origin, History, and Present Obligation. By the
Ven. Archdeacon Hessey, D.C.L. Fijth Edition. 7s. 6d.
Twilight of Life, The. Words of Counsel and Comfort for the
Aged. By the Rev. John Ellerton, M.A. is. 6d.
Voice of Time, The. By John Stkoud. Cloth gilt, is.
Selections from Cassell ^ Company's Publications.
<B6uratt0ttal Klorks antr ^tutrcjtta* iKanuala.
Agriculture Series, Cassell's. Edited by Professor Wrigiitson, Prin-
cipal of Downton Agricultural College. SOILS AND MANURES,
by Dr. J. Munro, is. 6d. ; CROPS, by Prof. Wrightson, is. 6d.
Alphabet, Cassell's Pictorial. 3s, 6d.
Arithmetics, The Modern School. By George Ricks, B.Sc. Lond.
With Test Cards. {List on application.)
Atlas, Cassell's Popular. Containing 24 Coloured Maps. 3s. 6d.
Book-Keeping. By Theodore Jonks. For Schools, 2S. ; cloth, 3s.
For the Million, 2S. ; cloth, 38. Books for Jones's System. 2s.
Botany in the Nineteenth Century, Commercial. By J. R. Jackson,
A.L.S., of the Royal Gardens, Kew. 3s. 6d.
■ ; - - ^- - - - Bvj. H. •
Classical Texts for Schools, Cassell's. {A List post free on application.)
Chemistry, The Public School. By J. H. Anderson, M.A. as. 6d.
Copy-Books, Cassell's Graduated. Eighte?.n Books, ad. each.
Copy-Books, The Modern School. Twelve Books, ad. each.
Drawing Copies, Cassell's Modern School Freehand. First Grade,
IS. ; Second Grade, as.
Drawing Copies, Cassell's "New Standard." Fourteen Books.
Books A to F for Standard* I. to IV., ad. each. Books G, H, K, L,
M, O, for Standards V. to VII., 3d. each. Books N and P, 4d. each.
Electricity, Practical. By Prof. W. E. Ayrton. 7s. 6d.
Energy and Motion. By William Paice, M.A. Illustrated, is. 6d.
English Literature, First Sketch of. By Prof. Morley. 7s. 6d.
English Literature, The Story of. By Anna Buckland. 3s. 6d.
Euclid, Cassell's. Edited by Prof. Wallace, M.A. is.
Euclid, The First Four Books of. New Edition. In paper, 6d. ; cloth, gd.
Experimental Geometry. By Paul Bert. Illustrated, is. 6d.
French, Cassell's Lessons in. New and Revised Edition. Parts I.
and II., each as. 6d. ; complete, 4s. 6d. Key, is. 6d.
French-English and English-French Dictionary. Entirely New
and Enlarg^ed Edition. 1,150 pages, 8vo, cloth, 38. 6d.
French Reader, Cassell's Public School. By G. S. Conrad, as. 6d.
Galbraith and Haughton's Scientific Manuals.
PlaneTrigonometry, as. 6d.— Euclid, Books I., II., III., as. 6d.— Books
IV., v., VI. , as. 6d.— Mathematical Tables, 3s. 6d.— Mechanics, 3s. 6d.
— Natural Philosophy, 3s. 6d. — Optics, as. 6d. — Hydrostatics, 3s. 6d. —
Astronomy, 5s.— Steam Engine, 3s. 6d. — Algebra, Part 1., cloth, as. 6d.;
Complete, 7s. 6d.— Tides and Tidal Currents, with Tidal Cards, 3s.
German Dictionary, Cassell's New. German-English, English-
German. Large Paper Edition^ 7s. 6d. ; Cheap Edition^ Cloth, 3s. 6d.
German of To-Day. By Dr. Heinemann. is. 6d.
German Reading, First Lessons in. By A. Jagst. Illustrated, is.
Guide to Employment for Boys. By W. S. Beard, F.R.G.S. is. 6d.
Hand-and-Eye Training. By G. Ricks, B.Sc. 2 Vols., with 16 Coloured
Plates in each Vol. Cr. 4to, 6s. each. Cards for Class Use, 5 sets, is. each.
Handbook of New Code of Regulations. New and Revised Edition.
By John F. Moss. is. ; cloth, as.
Historical Cartoons, Cassell's Coloured. Sire 45 in. x 35 in., as.
each. Mounted on canvas and varnished, with rollers, 58. each.
Historical Course for Schools, Cassell's. Illustrated throughout.
I.— Stories from English History, is. II.— The Simple Outline of
English History, is. 3d. III.— The Class History of England, as. 6d.
Latin-English and English-Latin Dictionary. By J. R. Beard,
D.D., and C. Beard, B.A. Crown 8vo, 914 pp., 3s. 6d.
Latin-English Dictionary, Cassell's. By J. R. V. Marchant, 3s. 6d.
Latin Piimer, The First. By Prof. Postgate. is.
Latin Primer, The New. By Prof. J. P. Postgate. Crown 8vo, as. 6d.
Latin Prose for Lower Forms. By M. A Baykield, M.A. as. 6d.
Selections from Cassell ^ Company s Publications.
Laundry Work for Schools. By Emma Lord. Pnce 6d.
Laws of Every-Day Life. By H. O. Arnold-Forster. is. 6d.
Little Folks* History of England. Illustrated, is. 6d. , ^ , ,
Making of the Home, The : A Book of Domestic Economy for School
and Home Use. By Mrs. Samuel A. Barnett. is. 6d.
Map-Building Series, Cassell's. Outline Maps prepared by H. O.
Arnold-Forster. Per Set of Twelve, pric is.
Marlborough Books :— Arithmetic Examples, 3s. Arithmetic Rules, is. od.
French Exercises, 3s. 6d. French Grammar, 2S. 6d. German do., 3s. 6d.
Mechanics and Machine Design, Numerical Examples in Practical.
By R. G. Blaine, M.E. With Diagrams. Cloth, 2s. 6d.
" Model Joint" Wall Sheets, for Instruction in Manual Training. By
S. Barter. Eight Sheets, as. 6d. each.
Music, An Elementary Manual of. By Henry Leslie, is.
New Poetry Readers, Cassell's. Illustrated. 9 Books, price id. each.
Object Lessons from Nature. By Prof. L. C. Miall, F.L.S. 2s. 6d.
Popular Educator, Cassell's NEW. With Revised Text, New Maps,
New Coloured Plates, New Type, &c. To be completed inSVols. ss.each.
Popular Educator, Cassell's. Complete in Six Vols., 5s. each.
Readers, Cassell's "Higher Class." {List on application.)
Readers, Cassell's Historical. Illustrated throughout, printed on
superior paper, and strongly bound in cloth. {List on application.')
Readers, Cassell's Readable. Carefully graduated, extremely in-
teresting, and illustrated throiighout. {List on application.)
Readers for Infant Schools, Coloured. Three Books. 4d. each.
Reader, The Citizen. By H. O, Arnold-Forster. Illustrated, is. 6d.
Reader, The Temperance. By Rev. J. Dennis Hird. Cr. 8vo, is. 6d.
Readers, The " Modern School " Geographical. {List on application.)
Readers, The " Modern School." Illustrated. [List on application.)
Reckoning, Howard's Anglo-American Art of. By C. Frusher
Howard. Paper covers, is. ; cloth, as.
Science Applied to Work. By J. A. Bower, is.
Science of Everyday Life. By John A. Bower. Illustrated, is.
Shade from Models, Common Objects, and Casts of Ornament,
How to. By W. E. Sparkes. With 25 Plates by the Author. Price 3S.6d.
Shakspere's Plays for School Use. 5 Books. Illustrated, 6d. each.
Shakspere Reading Book, The. Illustrated. 3s. 6d.
Spelling, A Complete Manual of. By J. D. Morell, LL.D. is.
Technical Manuals, Cassell's. Illustrated throughout :—
Handrailing and Staircasing, 3s. 6d. — Bricklayers, Drawing for, 3s. —
Building Construction, 2S.— Cabinet-Makers, Drawing for, 3s.— Car-
penters and Joiners, Drawing for, 3s. 6d. — Gothic Stonework, 3s.
— Linear Drawing and Practical Geometry, 2s. — Linear Drawing and
Projection. The Two Vols, in One, 3s. 6d.— Machinists and Engineers,
Drawing for, 4s. 6d. — Metal-Plate Workers, Drawing for, 3s. — Model
Drawing, 3s. — Orthographical and Isometrical Projection, 2s. — Practical
Perspective, 3s.— Stonemasons, Drawing for, 3s. — Applied Mechanics,
by Sir R. S. Ball, LL.D., 2s.— Systematic Drawing and Shading, 2s.
Technical Educator, Cassell's. Revised Edition. Four Vols., 55. each.
Technologfy, Manuals of. Edited by Prof. Avrton, F.R.S., and
Richard Wormell, D.Sc, M.A. Illustrated throughout :—
The Dyeing of Textile Fabrics, by Prof Hummel. 5s. — Watch and
Clock Making, by D. Glasgow, 4s. 6d.— Steel and Iron, by Prof. W. H.
Greenwood, F.C.S., M.I.C.E., &c., 5s.— Spinning Woollen and
Worsted, by W. S. B. McLaren, M.P., 4s. 6d.— Design in Textile
Fabrics, by T. R. Ashenhurst, 4s. 6d. — Practical Mechanics, by Prof.
Perry, M.E., 3s. 6d. — Cutting Tools Worked by Hand and Machine,
by Prof. Smith, 3s. 6d. {A Prospectus on application.)
Test Cards, Cassell's Combination. In sets, is. each.
Test Cards, " Modern School," Cassell's. In Sets, is. each.
CASSELL & COMPANY, Limited, Ludgate Hill, London.
Selections from Cassell f Company's Publications.
go0hs for f xmtt0 ^people.
"Little Folks " Half-Yearly Volume. Containing 432 4to pages, with
about 200 Illustrations, and Pictures in Colour. Boards, 3S.6d. ; cloth, 5s.
Bo-Peep. A Book for the Little Ones. With Original Stories and Verses.
Illustrated throughout. Yearly Volume. Boards, 2s. 6d. ; cloth, 3s. 6d.
Cassell's Pictorial Scrap Book, containing several thousand Pictures
beautifully printed and handsomely bound in one large volume.
Coloured boards, 15s. ; cloth lettered', 2is. Also in Six Sectional Vols.,
3s. 6d. each.
Warned— a King: or, How Merle set the Nursery Rhymes to
Rights. By Maggie Browne. With Original Designs by Harry
FuRNiss. 3s. 6d.
The Many Stories of Jack and Jill. Consisting of 65,536 Tales. By
the Rev. F. Bennett. Illustrated. 2s. 6d.
Schoolroom Theatricals. By Arthur Waugh. Illustrated. 2s. 6d.
Flora's Feast. A Masque of Flowers. Penned and Pictured by Walter
Crane. With 40 Pages in Colours. 5s.
Legends for Lionel. With 40 Illustrations in Colourby Walter Crane. 5s.
"Little Folks" Painting Book, The New. ^ Containing nearly 350
Outline Illustrations suitable for Colouring. Price is, ; post free, is. 2d.
Little Mother Bunch. By Mrs. Molesworth. Illustrated. Cloth, 3s. 6d.
The New Children's Album. Fcap. 410, 320 pages. Illustrated
throughout. 3s. 6d.
The Tales of the Sixty Mandarins. By P. V. Ramaswami Raju.
With an Introduction by Prof. Henry Morley. Illustrated. 5s.
Books for Young People. Illustrated. Cloth gilt, 5s. each
The King's Command : A Story
for Girls. By Maggie Symington.
Under Bayard's Banner. By
Henry Fnth.
The Romance of Invention.
By James Burnley.
The Champion of Odin; or. Viking
Life in the Days of Old. By J.
Fred. Hodgetts.
Boimd by a Spell ; or. The Hunted
Witch of the Forest. By the
Hon. Mrs. Greene.
Books for Young People. Illustrated. Price 3s. 6d. each.
Polly : A New-Fashioned GirL
By L. T. Meade.
For Fortune and Glory: A Story
ol the Soudan War. By Lewis
Hough.
" Follow My Leader." By Talbot
Baines Reed. [Pitt.
The Cost of a Mistake. By Sarah
A World of Girls: The Story of
a School. By L. T. Meade.
Lost among WMte Africans. By
David Ker.
The Palace Beautiful. By L. T.
Meade.
On Board the "Esmeralda." By
John C. Hutcheson.
In Quest of Gold. By A. St. Jolin-
ston.
For Queen and King. By Henry
Frith.
Books for Young People. Price 2S. 6d. each.
Heroes of Every-day Life. By
Laura Lane. Illustrated.
Decisive Events in History. By
Thomas Archer. With Origin^
Illustrations.
The True Bobinson Crusoes.
Early Explorers.
Home Chat with our Toung Folks.
Illustrated throughout
Jungle, Peak, and Plain. Illustrated
throughout.
The World's Lumber -Boom. By
Selina Gaye.
By Thomas Frost.
The "Cross and Crown" Series
2s.6d. each.
Strong to Suffer: A Story of
the Jews. By E. Wynne.
Heroes of the Indian. Empire:
or. Stories of Valour and
Victory. By Ernest Foster.
In Letters of Flame : A Story
of the Waldenses. By C. L.
Mat^aux.
Through Trial to Triumph. By
Madeline B. Hunt.
With Illustrations in each Book.
By Fire and Sword: A Story of
the Huguenots. By Thomas
Archer.
Adam Hepburn's Vow: A Tale of
Kirk and Covenant. By Annie
S. Swan.
No. XIII.; or, The Story of the
Lost Vestal. A Tale of Early
Christian Days. By Emma Mar-
Selections Jrom Cassell <|' Company's Publications.
••Golden Mottoes " Series, The. Each Book containing 208 pages, with
Four full-page Original Illustrations. Crown 8vo, cloth gilt, 2s. each.
' Honour is my O-uide." By Jeanie
' Nil DeBperandum." By the
Rev. F. Langbridge, M.A.
By Sarah
"Bear and Forbear,
Pitt.
"Foremost if I Can." By Helen
Atteridge.
Cheap Editions of Recent Popular Volumes for Young People,
Hering (Mrs. Adams-Acton).
Aim at a Sure End." By Emily
Searchfield.
He Conquers who Endiu-es." By
the Author of "May Cunningham's
Trial," &c.
Wild AdventTires in Wild
Places. By Dr. Gqrdon Stables,
R.N. Illustrated Price 2s. 6d.
Freedom's Sword : a Story of the
Days of Wallace and Bruce. By
Annie S. Swan. Price as. 6d.
Perils Afloat and Brigands Ashore.
By Alfred Elwes. Price as. 6d.
Pictures of School Life and Boy-
hood. Selected from the best Au-
thors. Edited by Percy Fitzgerald,
M.A. Price 2S.
z.
Modern Explorers. By Thomas Frost. Illustrated. Price 2s. 6d.
Books for Children. In Illuminated boards, fully Illustrated.
Twilight Fancies. 2s. 6d. | A Dozen and One. 5s.
Cheerful Clatter. 3s. ed. 1 Bible Talks. Ss.
Cassell 's Picture Story Books. Each containing Sixty Pages of
Pictures and Stories, &c. 6d. each.
liittle Talks.
Bright Stars.
Nursery Toys.
Pet's Posy.
Tiny Tales.
Daisy's Story Book.
Dot's Story Book.
A Neat of Stories.
G-ood-Night Stones.
Chats for Small Chatterers.
Auntie's Stories.
Birdie's Story Book,
liittle Cbimes.
A Sheaf of Tales.
Dewdrop Stories.
Cassell's Sixpenny Story Books. All Illustrated, and containing
Interesting Stories by well-known writers.
The Smuggler's Cave.
Little Lizzie.
Little Bird, Life and Adven-
tures o£
Luke Barnicott.
The Boat Club.
Little Pickles.
The Elohester College Boys.
My First Cruise.
The Little Peacemaker.
The Delft Jug.
Cassell's Shilling Story Books. All Illustrated, and containing Interest-
ing Stories.
Bunty and the Boys.
The Heir of Elmdale.
The Mystery at Shonollff
School.
Claimed at Last, and Boy's
Reward.
Thorns and Tangles.
The Cuckoo in the Bobin's Nest.
John's Mistake.
The History of Five Little
Pitchers.
Diamonds in the Sand.
Surly Bob.
The Giant's Cradle.
Shag and Doll.
Aunt Lucia's Looket.
The Magic Mirror.
The Cost of Revenge.
Clever Frank.
Among the Redskins.
The Ferryman of BrilL
Harry Maxwell.
A Banished Monarch.
Seventeen Cats.
Illustrated Books for the Little Ones. Containing interesting Stories.
All Illustrated, is. each ; cloth gilt, is. 6d.
Scrambles and Scrapes.
Tittle Tattle Tales.
Up and Down the Garden.
Sorts of Adventures.
Our Sunday Stories.
Our Holiday Hours.
Indoors and Out.
Some Farm Friends.
Wandering Ways.
Dumb Friends.
Those Golden Sands.
Little Mothers & their Children.
Our Pretty Pets.
Our Schoolday Hours.
Creatures Tame.
Creatures Wild.
Albums for Children. Price 3s. 6d. each.
The New Children's Album.
Illustrated throughout. Cloth.
The Album for Home, School,
and Play. Containing Stories by
Popular Authors. Set in bold
type, and Illustrated throughout
My Own Album of Animals. With
Full-page Illustrations.
Picture Album of All Sorts. With
Full-page Illustrations.
The Chit-Chat Album. lUustrated
throughout
Selections from Cassell ^ Company s Publications.
The ^Vo^ld's Workers. A Series of New and Original Volumes
With Portraits printed on a tint as Frontispiece, is. each.
By Rose
Dr. Arnold of Bugby.
E. Selfe.
The Earl of Sliaftesbury. By
Henry Frith.
Sarah Robinson, Agnes Wes-
ton, and Mrs. Meredith, By
E. M. Tomkinson.
Thomas A. Edison and Samuel
F. B. Morse. By Dr. Denslow
and J. Marsh Parker.
Mrs. Somerville and Mary Car-
penter. By Phyllis Browne.
General Gordon. By the Rev.
S. A. Swaine.
Charles uickens. By his Eldest
Daug-hter.
Sir Titus Salt and George
Moore. By J. Burnley.
David Livingstone. "
Smiles.
By Robert
Florence Nightingale, Catherine
Marsh, Prances Ridley Haver-
gal, Mrs. Ranyard ("L.N.R."j.
By Lizzie AUdridgre.
Dr. Guthrie, Father Mathew,
Elihu Burritt, George Livesey.
By John W. Kirton, LL.D.
Sir Henry HavelocK and Colin
CampbeU, Lord Clyde, By E. C,
Phillips.
Abraham Lincoln. By Ernest Foster,
George Mul er and Andrew Reed.
By E. R. Pitman.
Richard Cobden. By R. Gowinfr.
Benjamin Franklin. By E. M.
Tomkinson.
Handel. By Eliza Clarke. [Swaine.
Turner the Artist. By the Rev. S. A.
George and Robert Stephenson.
By C. L. .Mat6aux.
- %• The above IVorks {excluding RICHARD CoBDEN) can also be had Three in
One I'oL, cloth, gilt edges, -y.
Library of Wonders. Illustrated Gift-books for Boys. Paper, is. ;
cloth, IS. 6d.
Wonderful Adventures. I Wonders of Bodily Strength
Wonders of Animal Instinct. and SkiU.
Wonderful Balloon Ascents. | Wondertul Escapes.
Cassell 's Eighteenpenny Story Books. Illustrated.
Faith's Father.
Wee Willie Winkie.
Ups and Do wns of a Donkey's
Life.
Three Wee Ulster Lassies.
Tip the Ladder.
Dick's Hero ; and other Stories.
The Chip Boy.
Raggles, Baggies, and the
Emperor.
Roses from Thorns.
Gift Books for Young People.
Original Illustrations in each.
The Boy Hunters of Kentucky,
By Edward S,Ems.
Bed Feaihr: a Tale of the
By Land and Sea.
The Young Berringtona.
Jeff and Leff.
Tom Morris's Error.
Worth more than Gold,
" Through Flood— Through Fire; "
and other Stories,
The Girl with the Golden Looks,
Stories of the Olden Time,
With Four
American Frontier.
Edward S. Ellis.
By
By Popular Authors.
Cloth gilt, IS. 6d. each.
Major Monk's Motto. By the Rev.
F. Langrbridge.
Trixy. By Maggie Symington.
Rags and Rainbows: A Story of
Thanksgiving.
Uncle William's Charges; or. The
Broken Trust.
Pretty Pink's Purpose; or. The
Little Street Merchants.
Tim Thomson's Trial. By George
Weatherly.
Ursula's Stumbling-Block. By Julia
Goddard.
Ruth's Life-Work. By the Rev,
Joseph Johnson.
CasseU's Two-Shilling Story Books. Illustrated.
Stories of the Tower.
Mr. Burke's Nieces.
May Cunningham's Trial.
Seeking a City.
Rhoda's Reward; or,
Wishes were Horses."
Jack Marston's Anchor.
Frank's Life-Battle ; or
Three Friends.
Fritters. By Sarah Pitt.
The Two Hardcastles. By Made-
line Bonavia Hunt.
If
The
The Top of the Ladder : How to
Little Flotsam. [Reaoh it.
Madge and Her Friends,
The Children of the Court,
A Moonbeam Tangle.
Maid Marjory,
Peggy, and other Tales,
Books for Boys.
8bi£8, Sailors, and the Sea.
By R. J, Comewall-Jones. IHus-
■ 6*.
The Four Cats of the Tippertons.
Marion's Two Homes,
Little Folks' Sunday Book.
Two Fourpenny Bits.
Poor Nelly.
Tom Heribt.
Through Peril to Fortune.
Aunt Tabitha's Waifs.
In Mischief Again.
School Girls.
Famous Sailors of Former Times.
By Clements Markham. Illustrated,
aa.ed.
Selections from Cassell ^ Company's Publications.
NEW WORKS BY EDWARD S. ELLIS.
Lost in Samoa. A Tale of Adventure in the Navigator Islands. By
Edward S. Ellis. Illustrated. 3s. 6d.
Tad; or, "Getting Even" with Him. By Edward S. Ellis. Illus-
trated. 3s. 6d.
The "Deerfoot" Series. By Edward S. Ellis. With Four full-page
Illustrations in each Book. Cloth, bevelled boards, 2S. 6d. each.
The Hunters of the Ozark. | The Camp in the Mountains.
The Last War Trail.
The "Log Cabin" Series. By Edward S. Ellis. With Four Full-
page Illustrations in each. Crown 8vo, cloth, 2s. 6d. each.
The Lost Trail. | Camp-rire and Wigwam.
Footprints in the Forest.
The "Great River" Series. By Edward S. Ellis. Illustrated.
Crown 8vo, cloth, bevelled boards, 2s. 6d. each.
Down the Mississippi. | Lost in the Wilds.
Tip the Tapajos ; or. Adventures in Brazil.
The " Boy Pioneer" Series. By Edward S. Ellis. With Four Full-
page Illustrations in each Book. Crown 8vo, cloth, as. 6d. each.
Ned in the Woods. A Tale of I Ned on the Biver. A Tale of Indian
Early Days in the West. | River \Varfare.
Ned in the Block House. A Story of Pioneer Life in Kentucky.
The "World in Pictures
A Ramble Round France.
All the Russias.
Chats about G-ermany.
The Land of the Pyramids
(Egypt).
Feeps into China
Half-Crown Story Books.
Little Hinges.
Margaret's Enemy.
Pen's Perplexities.
Notable Snipwrecks.
Golden Days.
W^onders of Common Things
Truth will Out.
Illustrated throughout. 2s. 6d. each.
The Eastern Wonderland (Japan).
Q-limpses of South America.
Round Africa.
The Land of Temples (India).
The Isles of the Pacific.
Soldier and Patriot ((Jeorge Wash-
ington).
The Young Man in the Battle of
Life. By the Rev. Dr. Landels.
The True Glory of Woman. By the
Rev. Dr. Landels.
At the South Pole,
Three-and- Sixpenny Library of Standard Tales, &c. All Illus-
Ciown Svo. 3s. 6d. each.
Esther West.
Working to Win.
Krilof and his Fables. By W. R, S.
trated and bound in cloth gilt.
The Three Homes.
Deepdale Vicarage.
In Duty Bound.
The Half Sisters.
Peggy Oglivie's Inheritance.
The Family Honour.
Books for the Little Ones.
The Merry-go-Round. Poems for
Children. Illustrated. 5s.
Rhymes for the Young Folk.
By William Allingham. BeauiifuUy
Illustrated. 3s. 6d.
The Little Doings of some
Little Folks. By Chatty Cheer-
ful Illustrated. 5s.
The Pilgrim's Progress. With
Coloured Illustrations. 28. 6d.
Ralston, M.A.
Fairy Tales. By Prof. Morley.
The History Scrap Book; With
nearly i.ooo Engraving^s. 5s.: doth,
7b. 6d.
The Old Fairy Tales. With Original
Illustrations. Boards, Is.; cl., Is. 6d.
My Diary. With 12 Coloured Plates
and 366 Woodcuts. Is.
The Sunday Scrap Book. With
One Thousand Scripture Pictures.
Boards, 5b. ; cloth, 78. 6d,
Cassell & Company's Complete Catalogue will be sent post
free on application to
CASSELL & COMPANY, Limitkd, Ludgate Hill, London.
' A book without wHich no physical library can be held to be
complete."— Knowledge.
'All the useful applications of Electricity are described in its pages.
In that respect it has no rival."— English Mechanic.
Monthly, price 6d. {complete in 14 Parts, or One Volioiie).
Electricity in the Service
Ol JiLSlIIt A Popular and Practical Trea-
tise on the Applications of Electricity in Modern
Life. Translated and Edited, with Copious Additions,
from the German of Dr. Alfred Ritter von Urban-
ITZKY, by R. Wormell, D.Sc, M.A. With an Intro-
duction by Prof. John Perry, F.R.S. With nearly
850 lUustretions.
" This is a large work of 850 pages, profusely illustrated with 850 en-
gravings, all very clear and very instructive. The work is in two pans :
the first deals with Principles of Electricity, and resembles an ordinary
treatise on the subject brought up to date ; the second treats of the Tech-
nology of Electricity, and collects, classifies, and describes its modern
applications in a popular manner, but with great completeness. This
double method of proceeding solves a difficulty which presents itself in
connection with several sciences of recent development." — Educational
Times.
"This is a book without which no physical library can be held to be
complete, containing as it does between its two covers the sum and sub-
stance of numerous volumes. To the student it may be commended as an
admirably full and clear introduction to the science and art of Electricity ;
while to the advanced electrician it will be found of almost equal value as
a book of reference. It is furnished with that desideratum a capital index."
— Knowledge.
"A useful and valuable volume, if only from the fact that practically
all the useful applications of Electricity are described in its pages. In that
respect it has no rival." — English Alechanic.
"There is no more complete nanualof the practical application of
electrical science than is supplied by this volume, the text of which is
elucidated by about 850 capital \\\.\x%\.x?X\on'=>.''''— Manchester Examiner,
** It is doubtful whether the ordinary student of Electricity and the
educated reader in general could get a more satisfactory summary of this
great subject than Electricity in the Service of Man. Its accuracy
is perfect, its many-sidedness extraordinary, its condensation admirable,
and as a practical manual for all it is unsurpassed." — Boston {U.S.A.)
Beacon.
CA.SSELL & COMPANY, Limited, Lndsiate Hill, London.
Face End Matter. ] A
Numerical Examples in Practical Mechanics
and Machine Design.
By Robert Gordon Blaine, M.E., Senior Demonstrator,
the Mechanical Engineering Department, Finsbury Technical
College. With an Introduction by Professor John Perry,
M.E,, D.Sc, F.R.S. Twenty-six Diagrams. Price 2s. 6d.
CASSELL & COMPANY, Limited, Ludgate Hill, London.
MANUALS OF TECHNOLOGY
EDITED BY
Prot AYRTON, F.R.S., and RICHARD WORMELL, D.Sc, M.A.
The Dyeing of Textile Fabrics. — By j. j. Hummel, f.c.S.
With numerotis Diagrams. Price ^s.
Watch and Clock Making. — By D. Glasgow, Vice-President,
British Horological Institute. Price 4J-. 6d.
Steel and Iron. — By William Henry Greenwood, F.C.S.,
M.I.M.E., &c. With 97 Diagrams from Original Working Draw-
ings. Price 5j.
Spinning Woollen and Worsted. — By w. s. Bright McLaren,
M.P., Worsted Spinner. With 69 Diagrains. Price \s. 6d.
Cutting Tools. — By professor R. H. Smith. With 14 Folding Plates
and 5 1 Woodcuts. Price y. dd.
Practical Mechanics. — By Professor J. Perry, M.E. With numerous
Illustrations. Second Edition. Price 2,s. (>d.
Design in Textile Fabrics. — By T. R. Ashenhurst, Head Master,
Textile Department, Bradford Technical College. With lo Coloured
Plates and 106 Diagrams. Price \s. 6d.
CASSELL'S TECHNICAL MANUALS.
Illustrated throughout with Drawings and Working Diagrams, bound in Cloth.
Applied Mechanics. Cloth 2s.
Bricklayers, Drawing for. 3s.
Building Construction. 2s.
Cabinet-makers, Drawing for. 3s.
Carpenters and Joiners, Drawing
for. 3s. 6d.
Gothic Stonework. 3s,
Handrailing and Staircasing. 3s. 6d.
Linear Drawing and Practical Geo-
metry. 2S,
Linear Drawing and Projection.
The Two Vols, in One, 3s. 6d.
Machinists and Engineers, Drawing
for. 4s. 6d.
Metal-plate Workers, Drawing for.
Model Drawmg. 3s.
Orthographical and Isometrical
Projection. 2s.
Practical Perspective. 3s.
Stonemasons, Drawing for. Cloth.
3S-
Systematic Drawing and Shading.
CASSELL & COMPANY, Limited, Ludgate Hill, London.
To face cover 3.] 8 '
NAinr'* '*''"''
« «
to th
alrea
some
thepi._ _.-
IS more pleasantly i<
—Scotsman.
" It is full of accurate scientific information." — Manc/uster Exavtiner.
CASSELL & COMPANY, Limited, Ludgatt Hill, London.
Cover 3] c
idapted
at have
pursue
dge of
, no one
Jueiin'city."
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11